%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU108+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 : n017.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 14.21s 5.09s
% Output : Refutation 13.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 50
% Syntax : Number of formulae : 155 ( 70 unt; 0 typ; 7 def)
% Number of atoms : 388 ( 56 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 915 ( 108 ~; 28 |; 110 &; 613 @)
% ( 2 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 8 con; 0-3 aty)
% Number of variables : 204 ( 2 ^; 171 !; 24 ?; 204 :)
% ( 0 !>; 0 ?*; 0 @-; 7 @+)
% Comments :
%------------------------------------------------------------------------------
thf(preboolean_decl,type,
preboolean: $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(element_decl,type,
element: $i > $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(finite_decl,type,
finite: $i > $o ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subset_union2_decl,type,
subset_union2: $i > $i > $i > $i ).
thf(subset_difference_decl,type,
subset_difference: $i > $i > $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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk8_decl,type,
sk8: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( A @ powerset @ preboolean ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [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 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( @+[A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ) ) ) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_union2 ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k4_subset_1) ).
thf(153,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_union2 ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(8,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(61,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(58,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[58]) ).
thf(60,plain,
~ ( sk3 @ empty ),
inference(cnf,[status(esa)],[59]) ).
thf(195,plain,
( ( ( sk3 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,60]) ).
thf(196,plain,
( ( sk3 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[195]) ).
thf(197,plain,
sk3 != empty_set,
inference(simp,[status(thm)],[196]) ).
thf(42,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(170,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)],[42]) ).
thf(171,plain,
! [A: $i] :
( ( A @ sk12 @ finite )
& ( A @ sk12 @ natural )
& ( A @ sk12 @ ordinal )
& ( A @ sk12 @ epsilon_connected )
& ( A @ sk12 @ epsilon_transitive )
& ( A @ sk12 @ one_to_one )
& ( A @ sk12 @ function )
& ( A @ sk12 @ relation )
& ( A @ sk12 @ empty )
& ( A @ powerset @ ( A @ sk12 @ element ) ) ),
inference(cnf,[status(esa)],[170]) ).
thf(173,plain,
! [A: $i] : ( A @ sk12 @ epsilon_connected ),
inference(cnfConj,[status(thm)],[171]) ).
thf(176,plain,
! [A: $i] : ( A @ sk12 @ function ),
inference(cnfConj,[status(thm)],[171]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ element ) )
=> ( ( B @ ( A @ in ) )
| ( B @ empty ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ in ) )
| ( B @ empty )
| ~ ( B @ ( A @ element ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(175,plain,
! [A: $i] : ( A @ sk12 @ one_to_one ),
inference(cnfConj,[status(thm)],[171]) ).
thf(10,axiom,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_finset_1) ).
thf(64,plain,
? [A: $i] :
( ( A @ finite )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(65,plain,
( ( sk4 @ finite )
& ~ ( sk4 @ empty ) ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
~ ( sk4 @ empty ),
inference(cnfConj,[status(thm)],[65]) ).
thf(200,plain,
( ( ( sk4 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,66]) ).
thf(201,plain,
( ( sk4 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[200]) ).
thf(203,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[201]) ).
thf(16,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(83,plain,
! [A: $i,B: $i] :
( ( ( B @ finite )
& ( A @ finite ) )
=> ( B @ ( A @ set_union2 ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(23,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(101,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(18,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(88,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(30,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(120,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(51,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,plain,
sk2 @ empty,
inference(cnf,[status(esa)],[51]) ).
thf(198,plain,
( ( ( sk4 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,66]) ).
thf(199,plain,
( ( sk4 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[198]) ).
thf(202,plain,
sk4 != sk2,
inference(simp,[status(thm)],[199]) ).
thf(174,plain,
! [A: $i] : ( A @ sk12 @ empty ),
inference(cnfConj,[status(thm)],[171]) ).
thf(43,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(182,plain,
? [A: $i] :
( ( A @ preboolean )
& ( A @ diff_closed )
& ( A @ cap_closed )
& ( A @ cup_closed )
& ~ ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(183,plain,
( ( sk13 @ preboolean )
& ( sk13 @ diff_closed )
& ( sk13 @ cap_closed )
& ( sk13 @ cup_closed )
& ~ ( sk13 @ empty ) ),
inference(cnf,[status(esa)],[182]) ).
thf(185,plain,
~ ( sk13 @ empty ),
inference(cnfConj,[status(thm)],[183]) ).
thf(184,plain,
sk13 @ cup_closed,
inference(cnfConj,[status(thm)],[183]) ).
thf(31,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(125,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ( B @ finite )
& ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_subset_1) ).
thf(189,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( C @ ( B @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1,conjecture,
! [A: $i] : ( A @ powerset @ preboolean ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t20_finsub_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( A @ powerset @ preboolean ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(45,plain,
~ ! [A: $i] : ( A @ powerset @ preboolean ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,plain,
~ ( sk1 @ powerset @ preboolean ),
inference(cnf,[status(esa)],[45]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(93,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(55,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(56,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ? [B: $i] : ( A @ ( B @ set_union2 ) @ empty ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ set_union2 ) @ empty )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[56]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finsub_1) ).
thf(164,plain,
! [A: $i] :
( ( A @ preboolean )
=> ( ( A @ diff_closed )
& ( A @ cup_closed ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(179,plain,
! [A: $i] : ( A @ sk12 @ relation ),
inference(cnfConj,[status(thm)],[171]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(47,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(48,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(222,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ~ ( A @ powerset @ preboolean )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[50,46]) ).
thf(223,plain,
! [A: $i] :
( ~ ( A @ powerset @ preboolean )
| ~ ( sk1 @ empty )
| ~ ( A @ empty ) ),
inference(pattern_uni,[status(thm)],[222:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(478,plain,
! [A: $i] :
( ( ( sk2 @ empty )
!= ( A @ empty ) )
| ~ ( A @ powerset @ preboolean )
| ~ ( sk1 @ empty )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,223]) ).
thf(479,plain,
! [A: $i] :
( ( ( sk2 @ empty )
!= ( A @ empty ) )
| ~ ( A @ powerset @ preboolean )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[478]) ).
thf(480,plain,
( ~ ( sk2 @ powerset @ preboolean )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[479:[bind(A,$thf( sk2 ))]]) ).
thf(32,axiom,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
thf(130,plain,
! [A: $i] :
? [B: $i] :
( ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(131,plain,
! [A: $i] :
( ( A @ sk8 @ empty )
& ( A @ powerset @ ( A @ sk8 @ element ) ) ),
inference(cnf,[status(esa)],[130]) ).
thf(133,plain,
! [A: $i] : ( A @ sk8 @ empty ),
inference(cnfConj,[status(thm)],[131]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(74,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(85,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( B @ ( C @ ( A @ subset_union2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k4_subset_1) ).
thf(117,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_union2 ) ) )
= ( B @ ( C @ ( A @ subset_union2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(188,plain,
sk13 @ preboolean,
inference(cnfConj,[status(thm)],[183]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(77,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_finset_1) ).
thf(96,plain,
! [A: $i] :
( ( A @ empty )
=> ( A @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ powerset @ ( A @ element ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
thf(134,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)],[33]) ).
thf(25,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(105,plain,
! [A: $i,B: $i,C: $i] :
~ ( ( C @ empty )
& ( C @ powerset @ ( B @ element ) )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(292,plain,
( ( ( sk1 @ powerset @ preboolean )
!= ( sk13 @ preboolean ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[188,46]) ).
thf(293,plain,
( ( sk1 @ powerset @ preboolean )
!= ( sk13 @ preboolean ) ),
inference(simp,[status(thm)],[292]) ).
thf(298,plain,
( ( sk1 @ powerset )
!= sk13 ),
inference(simp,[status(thm)],[293]) ).
thf(39,axiom,
! [A: $i] :
~ ( A @ powerset @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
thf(161,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(180,plain,
! [A: $i] : ( A @ sk12 @ ordinal ),
inference(cnfConj,[status(thm)],[171]) ).
thf(12,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(71,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ element ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(181,plain,
! [A: $i] : ( A @ sk12 @ finite ),
inference(cnfConj,[status(thm)],[171]) ).
thf(38,axiom,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finsub_1) ).
thf(159,plain,
! [A: $i] :
( ( ( A @ diff_closed )
& ( A @ cup_closed ) )
=> ( A @ preboolean ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(187,plain,
sk13 @ cap_closed,
inference(cnfConj,[status(thm)],[183]) ).
thf(172,plain,
! [A: $i] : ( A @ sk12 @ natural ),
inference(cnfConj,[status(thm)],[171]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc12_finset_1) ).
thf(98,plain,
! [A: $i,B: $i] :
( ( A @ finite )
=> ( B @ ( A @ set_difference ) @ finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(204,plain,
( ( ( sk13 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,185]) ).
thf(205,plain,
( ( sk13 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[204]) ).
thf(208,plain,
sk13 != sk2,
inference(simp,[status(thm)],[205]) ).
thf(24,axiom,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
thf(103,plain,
! [A: $i] :
? [B: $i] : ( A @ ( B @ element ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(34,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(140,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)],[34]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(91,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
thf(155,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ? [B: $i] :
( ~ ( B @ empty )
& ( A @ powerset @ ( B @ element ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_union2 ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k4_subset_1) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( B @ ( B @ ( A @ subset_union2 ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(15,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(80,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(206,plain,
( ( ( sk13 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,185]) ).
thf(207,plain,
( ( sk13 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[206]) ).
thf(209,plain,
sk13 != empty_set,
inference(simp,[status(thm)],[207]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_subset_1) ).
thf(112,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( A @ powerset @ ( C @ ( B @ ( A @ subset_difference ) ) @ element ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(192,plain,
( ( ( sk3 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52,60]) ).
thf(193,plain,
( ( sk3 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[192]) ).
thf(194,plain,
sk3 != sk2,
inference(simp,[status(thm)],[193]) ).
thf(67,plain,
sk4 @ finite,
inference(cnfConj,[status(thm)],[65]) ).
thf(177,plain,
! [A: $i] : ( A @ sk12 @ epsilon_transitive ),
inference(cnfConj,[status(thm)],[171]) ).
thf(186,plain,
sk13 @ diff_closed,
inference(cnfConj,[status(thm)],[183]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k6_subset_1) ).
thf(114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ powerset @ ( C @ element ) )
& ( A @ powerset @ ( B @ element ) ) )
=> ( ( C @ ( B @ ( A @ subset_difference ) ) )
= ( C @ ( B @ set_difference ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(35,axiom,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_finset_1) ).
thf(151,plain,
! [A: $i] :
( ( A @ finite )
=> ! [B: $i] :
( ( A @ powerset @ ( B @ element ) )
=> ( B @ finite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,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(168,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)],[41]) ).
thf(162,plain,
~ ? [A: $i] : ( A @ powerset @ empty ),
inference(miniscope,[status(thm)],[161]) ).
thf(163,plain,
! [A: $i] :
~ ( A @ powerset @ empty ),
inference(cnf,[status(esa)],[162]) ).
thf(11,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(68,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(886,plain,
$false,
inference(e,[status(thm)],[153,197,173,176,63,175,203,58,83,101,88,170,120,202,174,185,52,184,125,189,46,93,57,164,179,480,61,133,74,85,60,117,188,53,77,96,134,105,298,45,161,64,180,71,54,181,159,187,172,98,208,103,140,91,66,155,108,130,223,80,209,112,194,50,67,177,182,186,55,114,151,168,51,47,163,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU108+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
% 0.22/0.47 % Computer : n017.cluster.edu
% 0.22/0.47 % Model : x86_64 x86_64
% 0.22/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.47 % Memory : 8046.5625MB
% 0.22/0.47 % OS : Linux 6.8.0-71-generic
% 0.22/0.47 % CPULimit : 300
% 0.22/0.47 % WCLimit : 300
% 0.22/0.47 % DateTime : Sat Sep 26 08:32:03 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.48 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
% 1.29/1.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.53 % [INFO] Parsing done (255ms).
% 1.94/1.55 % [INFO] Running in sequential loop mode.
% 3.14/2.16 % [INFO] eprover registered as external prover.
% 3.14/2.17 % [INFO] Scanning for conjecture ...
% 3.42/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 42 axioms. Running axiom selection ...
% 3.60/2.43 % [INFO] Axiom selection finished. Selected 42 axioms (removed 0 axioms).
% 3.83/2.54 % [INFO] Problem is first-order (TPTP FOF).
% 3.83/2.56 % [INFO] Type checking passed.
% 3.83/2.56 % [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 ...
% 14.21/5.08 % External prover 'e' found a proof!
% 14.21/5.08 % [INFO] Killing All external provers ...
% 14.21/5.09 % Time passed: 4403ms (effective reasoning time: 3531ms)
% 14.21/5.09 % 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)>
% 14.21/5.09 % Axioms used in derivation (42): cc2_finset_1, dt_k4_subset_1, rc1_subset_1, redefinition_k4_subset_1, commutativity_k4_subset_1, rc3_finset_1, t2_subset, idempotence_k2_xboole_0, antisymmetry_r2_hidden, rc4_finset_1, t1_boole, rc1_finsub_1, fc1_xboole_0, t1_subset, cc2_finsub_1, fc2_xboole_0, t6_boole, dt_k6_subset_1, rc2_subset_1, fc9_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, 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, redefinition_k6_subset_1, t10_finsub_1, idempotence_k4_subset_1, rc2_xboole_0
% 14.21/5.09 % No. of inferences in proof: 148
% 14.21/5.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4403 ms resp. 3531 ms w/o parsing
% 13.64/5.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.64/5.24 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------