%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU363+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 : n016.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 08:38:34 AM UTC 2026
% Result : Theorem 69.62s 14.63s
% Output : Refutation 69.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 39
% Syntax : Number of formulae : 80 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 226 ( 15 equ; 0 cnn)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 653 ( 24 ~; 2 |; 51 &; 483 @)
% ( 6 <=>; 87 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 2 con; 0-3 aty)
% Number of variables : 169 ( 0 ^; 147 !; 22 ?; 169 :)
% Comments :
%------------------------------------------------------------------------------
thf(rel_str_decl,type,
rel_str: $i > $o ).
thf(full_subrelstr_decl,type,
full_subrelstr: $i > $i > $o ).
thf(subrelstr_decl,type,
subrelstr: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(the_carrier_decl,type,
the_carrier: $i > $i ).
thf(related_decl,type,
related: $i > $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(relation_of2_decl,type,
relation_of2: $i > $i > $i > $o ).
thf(empty_decl,type,
empty: $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(finite_decl,type,
finite: $i > $o ).
thf(one_sorted_str_decl,type,
one_sorted_str: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(relation_restriction_decl,type,
relation_restriction: $i > $i > $i ).
thf(relation_restriction_as_relation_of_decl,type,
relation_restriction_as_relation_of: $i > $i > $i ).
thf(cartesian_product2_decl,type,
cartesian_product2: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(the_InternalRel_decl,type,
the_InternalRel: $i > $i ).
thf(ordered_pair_decl,type,
ordered_pair: $i > $i > $i ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(69,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_0) ).
thf(115,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( B @ rel_str ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(37,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(157,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_restriction ) @ relation ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( A @ relation_restriction ) @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(97,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( ( A @ ( B @ full_subrelstr ) )
<=> ( ( B @ the_InternalRel )
= ( B @ the_carrier @ ( A @ the_InternalRel @ relation_restriction_as_relation_of ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_yellow_0) ).
thf(109,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ ( B @ subrelstr ) )
=> ( ( ( ( B @ the_InternalRel )
= ( B @ the_carrier @ ( A @ the_InternalRel @ relation_restriction_as_relation_of ) ) )
=> ( A @ ( B @ full_subrelstr ) ) )
& ( ( A @ ( B @ full_subrelstr ) )
=> ( ( B @ the_InternalRel )
= ( B @ the_carrier @ ( A @ the_InternalRel @ relation_restriction_as_relation_of ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(86,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,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(150,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( ( B @ ( A @ relation_restriction_as_relation_of ) )
= ( B @ ( A @ relation_restriction ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k1_toler_1) ).
thf(99,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( ( B @ ( A @ relation_restriction_as_relation_of ) )
= ( B @ ( A @ relation_restriction ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,axiom,
? [A: $i] : ( A @ rel_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_orders_2) ).
thf(139,plain,
? [A: $i] : ( A @ rel_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( B @ ( C @ relation_restriction ) @ ( A @ in ) )
<=> ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ relation )
=> ( ( ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) )
=> ( B @ ( C @ relation_restriction ) @ ( A @ in ) ) )
& ( ( B @ ( C @ relation_restriction ) @ ( A @ in ) )
=> ( ( B @ ( B @ cartesian_product2 ) @ ( A @ in ) )
& ( C @ ( A @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(131,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(106,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(25,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(121,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)],[25]) ).
thf(13,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(84,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ cartesian_product2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(89,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_yellow_0) ).
thf(133,plain,
! [A: $i] :
( ( A @ rel_str )
=> ? [B: $i] : ( A @ ( B @ subrelstr ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(60,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
thf(117,plain,
! [A: $i] :
( ( A @ rel_str )
=> ( A @ one_sorted_str ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(8,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(70,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2_as_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(27,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(129,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ cartesian_product2 ) @ powerset @ ( C @ element ) )
=> ( C @ relation ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ( A @ ( B @ subrelstr ) )
& ( A @ ( B @ full_subrelstr ) ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( B @ the_carrier @ ( F @ in ) )
& ( B @ the_carrier @ ( E @ in ) )
& ( D @ ( C @ ( A @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( F @ ( E @ ( B @ related ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_yellow_0) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ( A @ ( B @ subrelstr ) )
& ( A @ ( B @ full_subrelstr ) ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( B @ the_carrier @ ( F @ in ) )
& ( B @ the_carrier @ ( E @ in ) )
& ( D @ ( C @ ( A @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( F @ ( E @ ( B @ related ) ) ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(41,plain,
~ ! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( ( A @ ( B @ subrelstr ) )
& ( A @ ( B @ full_subrelstr ) ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ! [D: $i] :
( ( A @ the_carrier @ ( D @ element ) )
=> ! [E: $i] :
( ( B @ the_carrier @ ( E @ element ) )
=> ! [F: $i] :
( ( B @ the_carrier @ ( F @ element ) )
=> ( ( ( B @ the_carrier @ ( F @ in ) )
& ( B @ the_carrier @ ( E @ in ) )
& ( D @ ( C @ ( A @ related ) ) )
& ( F = D )
& ( E = C ) )
=> ( F @ ( E @ ( B @ related ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(39,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(166,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(64,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( B @ ( B @ ( A @ relation_restriction_as_relation_of ) @ relation_of2_as_subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k1_toler_1) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( A @ relation )
=> ( B @ ( B @ ( B @ ( A @ relation_restriction_as_relation_of ) @ relation_of2_as_subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
? [A: $i] : ( A @ one_sorted_str ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_l1_struct_0) ).
thf(76,plain,
? [A: $i] : ( A @ one_sorted_str ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,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(103,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(16,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(91,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)],[16]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(66,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,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(155,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)],[36]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( C @ ( B @ ( A @ related ) ) )
<=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_orders_2) ).
thf(162,plain,
! [A: $i] :
( ( A @ rel_str )
=> ! [B: $i] :
( ( A @ the_carrier @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ the_carrier @ ( C @ element ) )
=> ( ( ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) )
=> ( C @ ( B @ ( A @ related ) ) ) )
& ( ( C @ ( B @ ( A @ related ) ) )
=> ( A @ the_InternalRel @ ( C @ ( B @ ordered_pair ) @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ powerset @ ( A @ element ) ) )
& ( ( B @ powerset @ ( A @ element ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(9,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(72,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
<=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) )
=> ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) ) )
& ( ( D @ ( C @ cartesian_product2 ) @ ( B @ ( A @ ordered_pair ) @ in ) )
=> ( ( D @ ( B @ in ) )
& ( C @ ( A @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(24,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(119,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)],[24]) ).
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(58,plain,
! [A: $i,B: $i] :
? [C: $i] : ( B @ ( A @ ( C @ relation_of2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15065,plain,
$false,
inference(e,[status(thm)],[69,115,157,78,97,141,109,86,135,150,99,139,168,131,106,121,84,89,133,60,117,70,137,129,41,166,64,81,76,103,91,66,155,162,123,72,143,119,58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU363+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.42 % Computer : n016.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 09:24:31 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 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
% 1.08/1.09 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.64/1.30 % [INFO] Parsing done (216ms).
% 1.64/1.32 % [INFO] Running in sequential loop mode.
% 2.41/1.72 % [INFO] eprover registered as external prover.
% 2.41/1.72 % [INFO] Scanning for conjecture ...
% 2.60/1.84 % [INFO] Found a conjecture (or negated_conjecture) and 46 axioms. Running axiom selection ...
% 2.84/1.93 % [INFO] Axiom selection finished. Selected 38 axioms (removed 8 axioms).
% 2.84/1.99 % [INFO] Problem is first-order (TPTP FOF).
% 2.84/2.00 % [INFO] Type checking passed.
% 2.84/2.01 % [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 ...
% 69.62/14.62 % External prover 'e' found a proof!
% 69.62/14.62 % [INFO] Killing All external provers ...
% 69.62/14.62 % Time passed: 13989ms (effective reasoning time: 13298ms)
% 69.62/14.62 % 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)>
% 69.62/14.63 % Axioms used in derivation (38): redefinition_m2_relset_1, cc2_finset_1, rc4_finset_1, dt_u1_orders_2, d9_orders_2, t5_subset, existence_m1_relset_1, t4_subset, t106_zfmisc_1, existence_m2_relset_1, dt_l1_orders_2, reflexivity_r1_tarski, t2_subset, existence_l1_struct_0, antisymmetry_r2_hidden, fc1_xboole_0, t1_subset, dt_m2_relset_1, dt_k1_toler_1, t6_boole, d14_yellow_0, t7_boole, existence_l1_orders_2, redefinition_k1_toler_1, t3_subset, cc1_relset_1, existence_m1_subset_1, existence_m1_yellow_0, dt_m1_yellow_0, rc3_finset_1, rc1_finset_1, cc1_finset_1, dt_k2_wellord1, t16_wellord1, t8_boole, rc1_xboole_0, fc14_finset_1, rc2_xboole_0
% 69.62/14.63 % No. of inferences in proof: 80
% 69.62/14.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 13989 ms resp. 13298 ms w/o parsing
% 69.62/14.69 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 69.62/14.69 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------