%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n019.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 08:37:36 AM UTC 2026
% Result : Theorem 72.71s 15.29s
% Output : Refutation 62.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 48
% Syntax : Number of formulae : 98 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 232 ( 30 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 617 ( 43 ~; 2 |; 71 &; 440 @)
% ( 2 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 22 usr; 2 con; 0-2 aty)
% Number of variables : 170 ( 0 ^; 150 !; 20 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(empty_decl,type,
empty: $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(symmetric_difference_decl,type,
symmetric_difference: $i > $i > $i ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(preboolean_decl,type,
preboolean: $i > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(cup_closed_decl,type,
cup_closed: $i > $o ).
thf(diff_closed_decl,type,
diff_closed: $i > $o ).
thf(relation_decl,type,
relation: $i > $o ).
thf(function_decl,type,
function: $i > $o ).
thf(one_to_one_decl,type,
one_to_one: $i > $o ).
thf(epsilon_transitive_decl,type,
epsilon_transitive: $i > $o ).
thf(epsilon_connected_decl,type,
epsilon_connected: $i > $o ).
thf(ordinal_decl,type,
ordinal: $i > $o ).
thf(natural_decl,type,
natural: $i > $o ).
thf(cap_closed_decl,type,
cap_closed: $i > $o ).
thf(14,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(88,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
thf(170,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(56,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ symmetric_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc17_finset_1) ).
thf(106,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ symmetric_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) @ ( A @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t100_xboole_1) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) @ ( A @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(59,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
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(108,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(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(123,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,conjecture,
! [A: $i] :
( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_union2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_union2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(50,plain,
~ ! [A: $i] :
( ~ ( A @ empty )
=> ( ! [B: $i] :
( ( A @ ( B @ element ) )
=> ! [C: $i] :
( ( A @ ( C @ element ) )
=> ( ( A @ ( C @ ( B @ set_union2 ) @ in ) )
& ( A @ ( C @ ( B @ symmetric_difference ) @ in ) ) ) ) )
=> ( A @ preboolean ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(175,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)],[42]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(104,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(44,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(184,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(26,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(125,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ preboolean )
<=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( ( A @ ( C @ ( B @ set_difference ) @ in ) )
& ( A @ ( C @ ( B @ set_union2 ) @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_finsub_1) ).
thf(93,plain,
! [A: $i] :
( ( ! [B: $i,C: $i] :
( ( ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( ( A @ ( C @ ( B @ set_difference ) @ in ) )
& ( A @ ( C @ ( B @ set_union2 ) @ in ) ) ) )
=> ( A @ preboolean ) )
& ( ( A @ preboolean )
=> ! [B: $i,C: $i] :
( ( ( A @ ( C @ in ) )
& ( A @ ( B @ in ) ) )
=> ( ( A @ ( C @ ( B @ set_difference ) @ in ) )
& ( A @ ( C @ ( B @ set_union2 ) @ in ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(78,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(33,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(147,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)],[33]) ).
thf(28,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(116,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(137,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(38,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(165,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(36,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(156,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( B @ ( A @ set_union2 ) @ ( B @ ( A @ symmetric_difference ) @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t95_xboole_1) ).
thf(141,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( B @ ( A @ set_union2 ) @ ( B @ ( A @ symmetric_difference ) @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(47,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).
thf(193,plain,
! [A: $i] :
? [B: $i] :
( ( B @ finite )
& ( B @ natural )
& ( B @ ordinal )
& ( B @ epsilon_connected )
& ( B @ epsilon_transitive )
& ( B @ one_to_one )
& ( B @ function )
& ( B @ relation )
& ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(212,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc9_finset_1) ).
thf(173,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(27,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(129,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(73,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,axiom,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finsub_1) ).
thf(205,plain,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(37,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(161,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(34,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(149,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(144,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).
thf(181,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ set_difference ) @ ( B @ ( A @ set_difference ) @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(187,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(12,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(81,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(135,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ symmetric_difference ) )
= ( A @ ( B @ symmetric_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(75,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(23,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(119,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
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(151,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(46,axiom,
! [A: $i] :
( ( empty_set @ ( A @ symmetric_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_boole) ).
thf(190,plain,
! [A: $i] :
( ( empty_set @ ( A @ symmetric_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc10_finset_1) ).
thf(68,plain,
! [A: $i,B: $i] :
( ( B @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc11_finset_1) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_intersection2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(24,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(122,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(90,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(111,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24372,plain,
$false,
inference(e,[status(thm)],[88,170,56,106,85,65,59,108,123,50,175,104,114,184,125,93,78,147,133,116,70,137,165,156,141,193,212,173,129,73,205,161,149,144,181,187,81,135,167,75,119,151,190,68,62,122,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU106+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.11 % 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
% 0.23/0.49 % Computer : n019.cluster.edu
% 0.23/0.49 % Model : x86_64 x86_64
% 0.23/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49 % Memory : 8046.5625MB
% 0.23/0.49 % OS : Linux 6.8.0-71-generic
% 0.23/0.49 % CPULimit : 300
% 0.23/0.49 % WCLimit : 300
% 0.23/0.49 % DateTime : Sat Sep 26 08:36:48 UTC 2026
% 0.23/0.49 % CPUTime :
% 0.23/0.49 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
% 1.45/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.99/1.66 % [INFO] Parsing done (317ms).
% 1.99/1.68 % [INFO] Running in sequential loop mode.
% 3.06/2.29 % [INFO] eprover registered as external prover.
% 3.28/2.30 % [INFO] Scanning for conjecture ...
% 3.50/2.46 % [INFO] Found a conjecture (or negated_conjecture) and 47 axioms. Running axiom selection ...
% 3.68/2.59 % [INFO] Axiom selection finished. Selected 47 axioms (removed 0 axioms).
% 3.89/2.69 % [INFO] Problem is first-order (TPTP FOF).
% 4.15/2.71 % [INFO] Type checking passed.
% 4.15/2.71 % [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 ...
% 72.71/15.29 % External prover 'e' found a proof!
% 72.71/15.29 % [INFO] Killing All external provers ...
% 72.71/15.29 % Time passed: 14583ms (effective reasoning time: 13603ms)
% 72.71/15.29 % 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)>
% 72.71/15.29 % Axioms used in derivation (47): t5_boole, cc2_finset_1, t2_boole, commutativity_k5_xboole_0, rc1_subset_1, d6_xboole_0, rc3_finset_1, t2_subset, idempotence_k2_xboole_0, rc2_xboole_0, antisymmetry_r2_hidden, idempotence_k3_xboole_0, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, t95_xboole_1, commutativity_k3_xboole_0, fc11_finset_1, cc2_finsub_1, fc2_xboole_0, fc10_finset_1, t6_boole, rc2_subset_1, fc9_finset_1, fc17_finset_1, commutativity_k2_xboole_0, t5_subset, t4_boole, t4_subset, fc3_xboole_0, t7_boole, fc1_subset_1, t3_subset, existence_m1_subset_1, t100_xboole_1, cc1_finsub_1, rc2_finset_1, reflexivity_r1_tarski, rc1_finset_1, cc1_finset_1, fc12_finset_1, t8_boole, rc1_xboole_0, t3_boole, t10_finsub_1
% 72.71/15.29 % No. of inferences in proof: 98
% 72.71/15.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 14583 ms resp. 13603 ms w/o parsing
% 62.78/15.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 62.78/15.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------