%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU382+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 : n010.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 08:38:38 AM UTC 2026
% Result : Theorem 9.79s 3.80s
% Output : Refutation 10.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 80
% Syntax : Number of formulae : 162 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 834 ( 19 equ; 0 cnn)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 1950 ( 150 ~; 2 |; 526 &;1128 @)
% ( 2 <=>; 142 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 43 ( 41 usr; 2 con; 0-3 aty)
% Number of variables : 222 ( 0 ^; 180 !; 42 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(boole_POSet_decl,type,
boole_POSet: $i > $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(empty_carrier_decl,type,
empty_carrier: $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(empty_decl,type,
empty: $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(heyting_relstr_decl,type,
heyting_relstr: $i > $o ).
thf(transitive_relstr_decl,type,
transitive_relstr: $i > $o ).
thf(antisymmetric_relstr_decl,type,
antisymmetric_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(v1_yellow_3_decl,type,
v1_yellow_3: $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(strict_rel_str_decl,type,
strict_rel_str: $i > $o ).
thf(incl_POSet_decl,type,
incl_POSet: $i > $i ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(relation_of2_as_subset_decl,type,
relation_of2_as_subset: $i > $i > $i > $o ).
thf(distributive_relstr_decl,type,
distributive_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(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(inclusion_order_decl,type,
inclusion_order: $i > $i ).
thf(reflexive_decl,type,
reflexive: $i > $o ).
thf(antisymmetric_decl,type,
antisymmetric: $i > $o ).
thf(transitive_decl,type,
transitive: $i > $o ).
thf(v1_partfun1_decl,type,
v1_partfun1: $i > $i > $i > $o ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(relation_decl,type,
relation: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(55,axiom,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_struct_0) ).
thf(385,plain,
? [A: $i] :
( ~ ( A @ empty_carrier )
& ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_yellow_1) ).
thf(288,plain,
! [A: $i] :
( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(56,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str )
& ~ ( A @ incl_POSet @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_yellow_1) ).
thf(389,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ( ( A @ incl_POSet @ antisymmetric_relstr )
& ( A @ incl_POSet @ transitive_relstr )
& ( A @ incl_POSet @ reflexive_relstr )
& ( A @ incl_POSet @ strict_rel_str )
& ~ ( A @ incl_POSet @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(81,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(569,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)],[81]) ).
thf(48,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(343,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)],[48]) ).
thf(19,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(159,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc7_waybel_1) ).
thf(167,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ upper_bounded_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ~ ( A @ v1_yellow_3 )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc3_yellow_3) ).
thf(151,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ~ ( A @ v1_yellow_3 )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(42,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(309,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(12,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(138,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( 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',cc5_waybel_1) ).
thf(101,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( 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)],[8]) ).
thf(68,axiom,
! [A: $i] :
( ( A @ boole_POSet @ distributive_relstr )
& ( 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 @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_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_1) ).
thf(479,plain,
! [A: $i] :
( ( A @ boole_POSet @ distributive_relstr )
& ( 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 @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_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)],[68]) ).
thf(72,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(518,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(58,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(408,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)],[58]) ).
thf(70,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(511,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)],[70]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(36,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(276,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)],[36]) ).
thf(78,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(559,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(5,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(93,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(61,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(416,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_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',cc8_waybel_1) ).
thf(316,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_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)],[45]) ).
thf(57,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(396,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)],[57]) ).
thf(34,axiom,
? [A: $i] :
( ~ ( A @ v1_yellow_3 )
& ( 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_3) ).
thf(265,plain,
? [A: $i] :
( ~ ( A @ v1_yellow_3 )
& ( 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)],[34]) ).
thf(75,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(527,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)],[75]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ~ ( A @ v1_yellow_3 )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_yellow_3) ).
thf(312,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ~ ( A @ v1_yellow_3 )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(54,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(380,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)],[54]) ).
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(85,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ incl_POSet )
= ( A @ inclusion_order @ ( A @ rel_str_of ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow_1) ).
thf(302,plain,
! [A: $i] :
( ( A @ incl_POSet )
= ( A @ inclusion_order @ ( A @ rel_str_of ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ( 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 @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_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',fc9_waybel_1) ).
thf(424,plain,
! [A: $i] :
( ( A @ boole_POSet @ complemented_relstr )
& ( A @ boole_POSet @ distributive_relstr )
& ( 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 @ complete_relstr )
& ( A @ boole_POSet @ with_infima_relstr )
& ( A @ boole_POSet @ with_suprema_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)],[63]) ).
thf(80,axiom,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ powerset @ incl_POSet ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_yellow_1) ).
thf(566,plain,
! [A: $i] :
( ( A @ boole_POSet )
= ( A @ powerset @ incl_POSet ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_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',cc10_waybel_1) ).
thf(252,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ boolean_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_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)],[32]) ).
thf(73,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(522,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(64,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(456,plain,
! [A: $i] :
( ( ( A @ one_sorted_str )
& ~ ( A @ empty_carrier ) )
=> ~ ( A @ the_carrier @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(6,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(97,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,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(329,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ empty )
& ~ ( A @ empty ) )
=> ~ ( B @ ( A @ cartesian_product2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_2) ).
thf(109,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ complete_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ join_complete_relstr )
& ( A @ up_complete_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_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',cc9_waybel_1) ).
thf(225,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ with_infima_relstr )
& ( A @ with_suprema_relstr )
& ( A @ antisymmetric_relstr )
& ( A @ transitive_relstr )
& ( A @ reflexive_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_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)],[30]) ).
thf(67,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)],[67]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ distributive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc6_waybel_1) ).
thf(298,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( ( A @ heyting_relstr )
& ~ ( A @ empty_carrier ) )
=> ( ( A @ distributive_relstr )
& ~ ( A @ empty_carrier ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(412,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(71,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(513,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(161,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(149,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(25,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(187,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)],[25]) ).
thf(29,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(219,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)],[29]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_lattice3) ).
thf(274,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_suprema_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(69,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(509,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)],[69]) ).
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(535,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(13,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(140,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(155,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(26,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(198,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(76,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(531,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(52,axiom,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ v1_yellow_3 ) )
=> ( ( A @ the_InternalRel @ relation )
& ~ ( A @ the_InternalRel @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc13_yellow_3) ).
thf(374,plain,
! [A: $i] :
( ( ( A @ rel_str )
& ~ ( A @ v1_yellow_3 ) )
=> ( ( A @ the_InternalRel @ relation )
& ~ ( A @ the_InternalRel @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(10,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(123,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)],[10]) ).
thf(65,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(458,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)],[65]) ).
thf(37,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(282,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)],[37]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_lattice3) ).
thf(414,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ with_infima_relstr )
=> ~ ( A @ empty_carrier ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(33,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(263,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(47,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ inclusion_order @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ inclusion_order @ v1_partfun1 ) ) )
& ( A @ inclusion_order @ transitive )
& ( A @ inclusion_order @ antisymmetric )
& ( A @ inclusion_order @ reflexive ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_yellow_1) ).
thf(331,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ inclusion_order @ relation_of2_as_subset ) ) )
& ( A @ ( A @ ( A @ inclusion_order @ v1_partfun1 ) ) )
& ( A @ inclusion_order @ transitive )
& ( A @ inclusion_order @ antisymmetric )
& ( A @ inclusion_order @ reflexive ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(66,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(470,plain,
! [A: $i] :
( ( A @ boole_POSet @ rel_str )
& ( A @ boole_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(49,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(359,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)],[49]) ).
thf(44,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(314,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ incl_POSet @ rel_str )
& ( A @ incl_POSet @ strict_rel_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_yellow_1) ).
thf(143,plain,
! [A: $i] :
( ( A @ incl_POSet @ rel_str )
& ( A @ incl_POSet @ strict_rel_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,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(99,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)],[7]) ).
thf(50,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(363,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)],[50]) ).
thf(4,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(87,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)],[4]) ).
thf(74,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(524,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(51,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(368,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)],[51]) ).
thf(18,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(158,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(23,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(171,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)],[23]) ).
thf(62,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(418,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)],[62]) ).
thf(53,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(378,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ boole_POSet @ the_carrier )
= ( A @ powerset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_waybel_7) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ boole_POSet @ the_carrier )
= ( A @ powerset ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(82,plain,
~ ! [A: $i] :
( ( A @ boole_POSet @ the_carrier )
= ( A @ powerset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(79,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(564,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)],[79]) ).
thf(41,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(305,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)],[41]) ).
thf(31,axiom,
? [A: $i] :
( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_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',rc5_waybel_1) ).
thf(239,plain,
? [A: $i] :
( ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ upper_bounded_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(11,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ empty_carrier )
=> ( A @ v1_yellow_3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_yellow_3) ).
thf(136,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( ( A @ empty_carrier )
=> ( A @ v1_yellow_3 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,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(178,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)],[24]) ).
thf(21,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(163,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(27,axiom,
? [A: $i] :
( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_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',rc4_waybel_1) ).
thf(200,plain,
? [A: $i] :
( ( A @ boolean_relstr )
& ( A @ complemented_relstr )
& ( A @ heyting_relstr )
& ( A @ distributive_relstr )
& ( A @ bounded_relstr )
& ( A @ upper_bounded_relstr )
& ( A @ lower_bounded_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)],[27]) ).
thf(572,plain,
$false,
inference(e,[status(thm)],[385,288,389,569,343,159,167,151,309,138,101,479,518,408,511,217,276,559,93,416,316,396,265,527,312,380,85,302,424,566,252,522,456,97,329,109,225,476,298,412,513,161,149,187,219,274,509,535,140,155,198,531,374,123,458,282,414,263,331,470,359,314,143,99,363,87,524,368,158,171,418,378,82,564,305,239,136,178,163,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU382+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
% 0.14/0.40 % Computer : n010.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 09:23:46 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.47/1.28 % [INFO] Parsing done (280ms).
% 1.47/1.29 % [INFO] Running in sequential loop mode.
% 2.89/1.71 % [INFO] eprover registered as external prover.
% 2.89/1.72 % [INFO] Scanning for conjecture ...
% 3.13/1.85 % [INFO] Found a conjecture (or negated_conjecture) and 88 axioms. Running axiom selection ...
% 3.31/1.97 % [INFO] Axiom selection finished. Selected 79 axioms (removed 9 axioms).
% 3.75/2.11 % [INFO] Problem is first-order (TPTP FOF).
% 3.75/2.12 % [INFO] Type checking passed.
% 3.75/2.13 % [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 ...
% 9.31/3.79 % External prover 'e' found a proof!
% 9.31/3.79 % [INFO] Killing All external provers ...
% 9.31/3.80 % Time passed: 3250ms (effective reasoning time: 2498ms)
% 9.31/3.80 % 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)>
% 9.79/3.80 % Axioms used in derivation (79): redefinition_m2_relset_1, rc4_finset_1, fc4_subset_1, rc2_yellow_0, dt_u1_orders_2, rc1_lattice3, fc8_yellow_1, t4_subset, cc7_waybel_1, cc2_lattice3, cc10_waybel_1, cc2_finset_1, rc5_waybel_1, fc1_xboole_0, cc5_waybel_1, cc9_waybel_1, fc5_yellow_1, t1_subset, cc6_waybel_1, cc12_waybel_0, cc1_lattice3, dt_m2_relset_1, cc14_waybel_0, cc11_waybel_0, rc13_waybel_0, dt_k3_yellow_1, rc2_lattice3, t6_boole, rc2_subset_1, rc4_waybel_1, t5_subset, cc9_waybel_0, existence_m1_relset_1, t7_boole, existence_l1_orders_2, d1_yellow_1, fc9_waybel_1, rc3_struct_0, fc1_subset_1, cc13_waybel_0, dt_g1_orders_2, rc1_subset_1, cc1_yellow_2, fc6_yellow_1, abstractness_v1_orders_2, cc4_yellow_0, cc3_yellow_3, t3_subset, fc1_waybel_1, existence_m1_subset_1, dt_k2_yellow_1, existence_m2_relset_1, rc1_yellow_3, dt_l1_orders_2, free_g1_orders_2, fc1_struct_0, reflexivity_r1_tarski, cc1_yellow_3, cc8_waybel_1, cc10_waybel_0, cc5_yellow_0, rc3_finset_1, rc1_finset_1, cc1_finset_1, cc1_yellow_0, t8_boole, rc1_xboole_0, rc5_struct_0, t2_subset, t4_yellow_1, fc13_yellow_3, existence_l1_struct_0, fc7_yellow_1, fc14_finset_1, cc2_yellow_3, rc2_xboole_0, cc3_yellow_0, dt_k1_yellow_1, antisymmetry_r2_hidden
% 9.79/3.80 % No. of inferences in proof: 162
% 9.79/3.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3250 ms resp. 2498 ms w/o parsing
% 10.12/4.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.12/4.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------