%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU155+2 : 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 : n001.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 08:37:47 AM UTC 2026
% Result : Theorem 78.19s 17.05s
% Output : Refutation 66.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 81
% Syntax : Number of formulae : 249 ( 108 unt; 0 typ; 9 def)
% Number of atoms : 671 ( 270 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 1719 ( 194 ~; 101 |; 119 &;1140 @)
% ( 25 <=>; 140 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 486 ( 11 ^; 445 !; 21 ?; 486 :)
% ( 0 !>; 0 ?*; 0 @-; 9 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(union_decl,type,
union: $i > $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(proper_subset_decl,type,
proper_subset: $i > $i > $o ).
thf(powerset_decl,type,
powerset: $i > $i ).
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(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i > $o ).
thf(sk16_decl,type,
sk16: $i > $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ in ) )
=> ( A @ union @ ( sk1 @ subset ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ in ) ) ) ) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9_zfmisc_1) ).
thf(142,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_xboole_1) ).
thf(417,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l50_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(74,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ union @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(75,plain,
( ~ ( sk2 @ union @ ( sk1 @ subset ) )
& ( sk2 @ ( sk1 @ in ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(77,plain,
~ ( sk2 @ union @ ( sk1 @ subset ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(167,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(35,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(182,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(32,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(173,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(174,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(lifteq,[status(thm)],[174]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(101,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(72,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(478,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(479,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[478]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t33_xboole_1) ).
thf(352,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_difference ) @ ( C @ ( A @ set_difference ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(31,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)],[31]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(269,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l32_xboole_1) ).
thf(184,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(110,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(122,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(123,plain,
~ ? [A: $i] :
( ( A @ singleton )
= empty_set ),
inference(miniscope,[status(thm)],[122]) ).
thf(124,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(cnf,[status(esa)],[123]) ).
thf(125,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(lifteq,[status(thm)],[124]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(91,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(92,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[92]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
thf(271,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ! [D: $i] :
( ( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(272,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) )
=> ( C
= ( B @ ( A @ unordered_pair ) ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
=> ( ! [D: $i] :
( ( ( D = B )
| ( D = A ) )
=> ( C @ ( D @ in ) ) )
& ! [D: $i] :
( ( C @ ( D @ in ) )
=> ( ( D = B )
| ( D = A ) ) ) ) ) ),
inference(miniscope,[status(thm)],[271]) ).
thf(273,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( F @ ( G @ ( H @ sk17 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk15 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk17 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk17 ) ) )
= F )
| ( H @ ( G @ ( F @ sk15 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk15 ) ) )
| ( ( F @ ( G @ ( H @ sk16 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk15 ) ) )
| ( ( F @ ( G @ ( H @ sk16 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk15 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk16 ) ) @ in ) ) )
& ( ( C @ ( E @ in ) )
| ( E != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( C @ ( E @ in ) )
| ( E != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) )
& ( ( D = B )
| ( D = A )
| ~ ( C @ ( D @ in ) )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ) ),
inference(cnf,[status(esa)],[272]) ).
thf(279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[273]) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[279]) ).
thf(289,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[288]) ).
thf(70,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(448,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(78,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_xboole_1) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(34,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(179,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(614,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[479,77]) ).
thf(615,plain,
! [A: $i] :
( ( A @ ( empty_set @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[614]) ).
thf(620,plain,
! [A: $i] :
( ( A
!= ( sk2 @ union ) )
| ( sk1 != empty_set ) ),
inference(simp,[status(thm)],[615]) ).
thf(623,plain,
sk1 != empty_set,
inference(simp,[status(thm)],[620]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_zfmisc_1) ).
thf(106,plain,
! [A: $i,B: $i,C: $i,D: $i] :
~ ( ( A != D )
& ( A != C )
& ( ( B @ ( A @ unordered_pair ) )
= ( D @ ( C @ unordered_pair ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc3_xboole_0) ).
thf(84,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_difference ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_xboole_0) ).
thf(480,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_difference ) ) ) )
& ( ( C
= ( B @ ( A @ set_difference ) ) )
=> ! [D: $i] :
( ( ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ~ ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t63_xboole_1) ).
thf(396,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(87,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(88,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[87]) ).
thf(89,plain,
~ ( sk4 @ empty ),
inference(cnf,[status(esa)],[88]) ).
thf(16,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(116,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_union2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
thf(307,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_union2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_union2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
| ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(7,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(90,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(510,plain,
( ( ( sk4 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[90,89]) ).
thf(511,plain,
( ( sk4 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[510]) ).
thf(512,plain,
sk4 != empty_set,
inference(simp,[status(thm)],[511]) ).
thf(53,axiom,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l25_zfmisc_1) ).
thf(366,plain,
! [A: $i,B: $i] :
~ ( ( B @ ( A @ in ) )
& ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(79,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[78]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(624,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != empty_set )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[81,623]) ).
thf(625,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( A @ empty )
| ~ ( sk1 @ empty ) ),
inference(pattern_uni,[status(thm)],[624:[bind(A,$thf( sk1 ))]]) ).
thf(628,plain,
( ~ ( empty_set @ empty )
| ~ ( sk1 @ empty ) ),
inference(simp,[status(thm)],[625]) ).
thf(713,plain,
( ~ $true
| ~ ( sk1 @ empty ) ),
inference(rewrite,[status(thm)],[628,90]) ).
thf(714,plain,
~ ( sk1 @ empty ),
inference(simp,[status(thm)],[713]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(334,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(37,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(192,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ( ! [C: $i] :
~ ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_xboole_0) ).
thf(137,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_xboole_1) ).
thf(435,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( C @ ( A @ set_union2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_zfmisc_1) ).
thf(94,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(95,plain,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( A @ singleton )
= ( C @ ( B @ unordered_pair ) ) )
=> ( A = B ) ),
inference(miniscope,[status(thm)],[94]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( A @ singleton )
!= ( C @ ( B @ unordered_pair ) ) ) ),
inference(cnf,[status(esa)],[95]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( ( A @ singleton )
!= ( C @ ( B @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(198,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(199,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[198]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C = D )
| ~ ( C @ ( D @ subset ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A @ ( B @ subset ) )
| ( A != B ) )
& ( ( B @ ( A @ subset ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[199]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[200]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[201]) ).
thf(205,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[204]) ).
thf(694,plain,
! [A: $i] :
( ( ( A @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[205,77]) ).
thf(695,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
!= ( sk2 @ union @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[694]) ).
thf(696,plain,
! [A: $i] :
( ( A
!= ( sk2 @ union ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[695]) ).
thf(697,plain,
( ( sk2 @ union )
!= sk1 ),
inference(simp,[status(thm)],[696]) ).
thf(168,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(139,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(140,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(cnf,[status(esa)],[139]) ).
thf(141,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(lifteq,[status(thm)],[140]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_zfmisc_1) ).
thf(420,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(76,plain,
sk2 @ ( sk1 @ in ),
inference(cnfConj,[status(thm)],[75]) ).
thf(44,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(298,plain,
! [A: $i] :
( ( ! [B: $i] :
~ ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ( ( A = empty_set )
=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(299,plain,
( ! [A: $i] :
( ~ ? [B: $i] : ( A @ ( B @ in ) )
=> ( A = empty_set ) )
& ! [A: $i] :
( ( A = empty_set )
=> ~ ? [B: $i] : ( A @ ( B @ in ) ) ) ),
inference(miniscope,[status(thm)],[298]) ).
thf(300,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = empty_set )
| ( C @ ( C @ sk18 @ in ) ) )
& ( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ) ),
inference(cnf,[status(esa)],[299]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(cnfConj,[status(thm)],[300]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(lifteq,[status(thm)],[301]) ).
thf(304,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(simp,[status(thm)],[303]) ).
thf(602,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ in ) )
!= ( empty_set @ ( A @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,304]) ).
thf(603,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ in ) )
!= ( empty_set @ ( A @ in ) ) ),
inference(simp,[status(thm)],[602]) ).
thf(604,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[603]) ).
thf(607,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[604]) ).
thf(608,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != empty_set )
| ~ ( B @ empty )
| ~ ( A @ empty ) ),
inference(paramod_ordered,[status(thm)],[81,607]) ).
thf(609,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( A @ empty )
| ~ ( sk2 @ empty ) ),
inference(pattern_uni,[status(thm)],[608:[bind(A,$thf( sk2 ))]]) ).
thf(612,plain,
( ~ ( empty_set @ empty )
| ~ ( sk2 @ empty ) ),
inference(simp,[status(thm)],[609]) ).
thf(646,plain,
( ~ $true
| ~ ( sk2 @ empty ) ),
inference(rewrite,[status(thm)],[612,90]) ).
thf(647,plain,
~ ( sk2 @ empty ),
inference(simp,[status(thm)],[646]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l28_zfmisc_1) ).
thf(371,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(20,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ proper_subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(134,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(360,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_xboole_1) ).
thf(398,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(62,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(412,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
<=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).
thf(425,plain,
! [A: $i,B: $i] :
( ( ( ( A != B )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ proper_subset ) ) )
& ( ( B @ ( A @ proper_subset ) )
=> ( ( A != B )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(25,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(148,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ powerset ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( A @ ( C @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) )
=> ( B
= ( A @ powerset ) ) )
& ( ( B
= ( A @ powerset ) )
=> ! [C: $i] :
( ( ( A @ ( C @ subset ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( A @ ( C @ subset ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(33,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(176,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_xboole_1) ).
thf(423,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( B @ set_intersection2 ) @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(117,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(cnf,[status(esa)],[116]) ).
thf(118,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(lifteq,[status(thm)],[117]) ).
thf(85,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ? [B: $i] : ( A @ ( B @ set_union2 ) @ empty ) ),
inference(miniscope,[status(thm)],[84]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ set_union2 ) @ empty )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[85]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t40_xboole_1) ).
thf(159,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l23_zfmisc_1) ).
thf(406,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(113,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(82,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(83,plain,
sk3 @ empty,
inference(cnf,[status(esa)],[82]) ).
thf(507,plain,
( ( ( sk4 @ empty )
!= ( sk3 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,89]) ).
thf(508,plain,
( ( sk4 @ empty )
!= ( sk3 @ empty ) ),
inference(simp,[status(thm)],[507]) ).
thf(509,plain,
sk4 != sk3,
inference(simp,[status(thm)],[508]) ).
thf(10,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(98,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ set_intersection2 ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(451,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) )
=> ( C
= ( B @ ( A @ set_intersection2 ) ) ) )
& ( ( C
= ( B @ ( A @ set_intersection2 ) ) )
=> ! [D: $i] :
( ( ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) )
=> ( C @ ( D @ in ) ) )
& ( ( C @ ( D @ in ) )
=> ( ( B @ ( D @ in ) )
& ( A @ ( D @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_0) ).
thf(345,plain,
! [A: $i,B: $i] :
( ~ ( ( B @ ( A @ disjoint ) )
& ? [C: $i] :
( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) ) )
& ~ ( ! [C: $i] :
~ ( ( B @ ( C @ in ) )
& ( A @ ( C @ in ) ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_xboole_1) ).
thf(103,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(723,plain,
( ( ( sk3 @ empty )
!= ( sk1 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,714]) ).
thf(724,plain,
( ( sk3 @ empty )
!= ( sk1 @ empty ) ),
inference(simp,[status(thm)],[723]) ).
thf(726,plain,
sk3 != sk1,
inference(simp,[status(thm)],[724]) ).
thf(28,axiom,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).
thf(162,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(111,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(cnf,[status(esa)],[110]) ).
thf(112,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(lifteq,[status(thm)],[111]) ).
thf(50,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_zfmisc_1) ).
thf(355,plain,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ singleton @ subset ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(24,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(145,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(149,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[148]) ).
thf(150,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[149]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t26_xboole_1) ).
thf(409,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ subset ) )
=> ( C @ ( B @ set_intersection2 ) @ ( C @ ( A @ set_intersection2 ) @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(40,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ in ) )
<=> ( B @ ( C @ in ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_tarski) ).
thf(231,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( ( B @ ( C @ in ) )
=> ( A @ ( C @ in ) ) )
& ( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(119,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).
thf(151,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_intersection2 ) )
= empty_set )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= empty_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(cnf,[status(esa)],[98]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(lifteq,[status(thm)],[99]) ).
thf(853,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( empty_set @ ( C @ set_intersection2 ) ) )
| ( ( A @ ( B @ set_intersection2 ) )
= empty_set ) ),
inference(paramod_ordered,[status(thm)],[100,175]) ).
thf(854,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_intersection2 ) )
= empty_set ),
inference(pattern_uni,[status(thm)],[853:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( A ))]]) ).
thf(183,plain,
! [B: $i,A: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(cnf,[status(esa)],[182]) ).
thf(56,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(373,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).
thf(210,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ( ( B
= ( A @ singleton ) )
=> ! [C: $i] :
( ( ( C = A )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B
= ( A @ union ) )
<=> ! [C: $i] :
( ( B @ ( C @ in ) )
<=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_tarski) ).
thf(242,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) )
=> ( B
= ( A @ union ) ) )
& ( ( B
= ( A @ union ) )
=> ! [C: $i] :
( ( ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) )
=> ( B @ ( C @ in ) ) )
& ( ( B @ ( C @ in ) )
=> ? [D: $i] :
( ( A @ ( D @ in ) )
& ( D @ ( C @ in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).
thf(358,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(437,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(63,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(415,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(126,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ set_difference ) )
= A )
=> ( B @ ( A @ disjoint ) ) )
& ( ( B @ ( A @ disjoint ) )
=> ( ( B @ ( A @ set_difference ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(135,plain,
~ ? [A: $i] : ( A @ ( A @ proper_subset ) ),
inference(miniscope,[status(thm)],[134]) ).
thf(136,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(cnf,[status(esa)],[135]) ).
thf(163,plain,
( ( empty_set @ powerset )
= ( empty_set @ singleton ) ),
inference(lifteq,[status(thm)],[162]) ).
thf(54,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(369,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(656,plain,
( ( ( sk3 @ empty )
!= ( sk2 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[83,647]) ).
thf(657,plain,
( ( sk3 @ empty )
!= ( sk2 @ empty ) ),
inference(simp,[status(thm)],[656]) ).
thf(659,plain,
sk3 != sk2,
inference(simp,[status(thm)],[657]) ).
thf(211,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) )
=> ( B
= ( A @ singleton ) ) )
& ! [A: $i,B: $i] :
( ( B
= ( A @ singleton ) )
=> ( ! [C: $i] :
( ( C = A )
=> ( B @ ( C @ in ) ) )
& ! [C: $i] :
( ( B @ ( C @ in ) )
=> ( C = A ) ) ) ) ),
inference(miniscope,[status(thm)],[210]) ).
thf(212,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk7 ) @ in ) )
| ( ( E @ ( F @ sk6 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk7 ) )
= E )
| ( ( E @ ( F @ sk6 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk7 ) @ in ) )
| ( F @ ( E @ ( F @ sk6 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk7 ) )
= E )
| ( F @ ( E @ ( F @ sk6 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[211]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[212]) ).
thf(221,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[216]) ).
thf(222,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[221]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
thf(337,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ in ) )
=> ( B @ ( C @ in ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(20600,plain,
$false,
inference(e,[status(thm)],[142,417,77,167,182,175,101,479,352,170,269,184,110,125,93,289,448,78,164,179,623,106,84,480,396,89,116,74,307,512,366,714,334,192,137,435,97,697,169,141,420,647,173,371,134,360,205,398,298,412,425,148,375,176,423,118,86,159,406,113,81,509,98,271,451,76,345,103,726,91,198,162,112,355,145,150,409,231,87,304,139,119,478,82,151,854,183,373,210,242,358,437,94,415,126,136,163,369,607,90,83,659,222,100,337,122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU155+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.12 % 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
% 0.25/0.51 % Computer : n001.cluster.edu
% 0.25/0.51 % Model : x86_64 x86_64
% 0.25/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.51 % Memory : 8046.5625MB
% 0.25/0.51 % OS : Linux 6.8.0-71-generic
% 0.25/0.51 % CPULimit : 300
% 0.25/0.51 % WCLimit : 300
% 0.25/0.51 % DateTime : Sat Sep 26 08:47:13 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 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
% 1.42/1.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.25/1.71 % [INFO] Parsing done (340ms).
% 2.25/1.73 % [INFO] Running in sequential loop mode.
% 3.31/2.33 % [INFO] eprover registered as external prover.
% 3.31/2.34 % [INFO] Scanning for conjecture ...
% 3.74/2.51 % [INFO] Found a conjecture (or negated_conjecture) and 79 axioms. Running axiom selection ...
% 3.99/2.64 % [INFO] Axiom selection finished. Selected 71 axioms (removed 8 axioms).
% 4.22/2.78 % [INFO] Problem is first-order (TPTP FOF).
% 4.46/2.80 % [INFO] Type checking passed.
% 4.46/2.81 % [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 ...
% 77.74/17.04 % External prover 'e' found a proof!
% 77.74/17.05 % [INFO] Killing All external provers ...
% 78.19/17.05 % Time passed: 16334ms (effective reasoning time: 15312ms)
% 78.19/17.05 % 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)>
% 78.19/17.05 % Axioms used in derivation (71): fc1_xboole_0, t2_boole, d1_xboole_0, t6_boole, t9_zfmisc_1, l2_zfmisc_1, t19_xboole_1, t17_xboole_1, d1_tarski, idempotence_k3_xboole_0, t1_boole, t3_xboole_1, t37_xboole_1, commutativity_k3_xboole_0, d2_tarski, fc2_xboole_0, t1_xboole_1, commutativity_k2_xboole_0, t4_xboole_0, l25_zfmisc_1, t1_zfmisc_1, d8_xboole_0, t2_tarski, t33_xboole_1, l32_xboole_1, t8_zfmisc_1, t4_boole, fc3_xboole_0, d2_xboole_0, d4_tarski, t7_boole, t48_xboole_1, d7_xboole_0, t83_xboole_1, l28_zfmisc_1, l4_zfmisc_1, antisymmetry_r2_xboole_0, l3_zfmisc_1, commutativity_k2_tarski, d1_zfmisc_1, t69_enumset1, t26_xboole_1, t63_xboole_1, t8_xboole_1, t28_xboole_1, d3_tarski, reflexivity_r1_tarski, t6_zfmisc_1, t2_xboole_1, d4_xboole_0, t36_xboole_1, l23_zfmisc_1, t8_boole, rc1_xboole_0, t12_xboole_1, t10_zfmisc_1, symmetry_r1_xboole_0, idempotence_k2_xboole_0, d10_xboole_0, t7_xboole_1, t60_xboole_1, t3_xboole_0, t3_boole, rc2_xboole_0, t45_xboole_1, t40_xboole_1, l1_zfmisc_1, irreflexivity_r2_xboole_0, d3_xboole_0, t39_xboole_1, antisymmetry_r2_hidden
% 78.19/17.05 % No. of inferences in proof: 240
% 78.19/17.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 16334 ms resp. 15312 ms w/o parsing
% 66.38/17.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 66.38/17.25 % [INFO] Killing All external provers ...
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