%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:30:45 AM UTC 2026
% Result : Theorem 18.84s 5.79s
% Output : Refutation 17.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 153 ( 41 unt; 0 typ; 4 def)
% Number of atoms : 486 ( 129 equ; 0 cnn)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 1385 ( 198 ~; 138 |; 44 &; 946 @)
% ( 10 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 16 usr; 5 con; 0-2 aty)
% Number of variables : 380 ( 4 ^; 368 !; 4 ?; 380 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(sum_decl,type,
sum: $i > $i ).
thf(product_decl,type,
product: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ subset ) )
=> ( empty_set @ ( A @ ( A @ ( B @ difference ) @ intersection ) @ equal_set ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( A @ ( sk1 @ subset ) )
=> ( empty_set @ ( sk1 @ ( sk1 @ ( A @ difference ) @ intersection ) @ equal_set ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ member ) )
=> ( C @ ( B @ member ) ) ) ) ) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( B @ singleton @ ( A @ member ) ) )
& ( ( B @ singleton @ ( A @ member ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(65,plain,
( ! [A: $i,B: $i] :
( ( A = B )
=> ( B @ singleton @ ( A @ member ) ) )
& ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ member ) )
=> ( A = B ) ) ),
inference(miniscope,[status(thm)],[64]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ singleton @ ( C @ member ) )
| ( C != D ) )
& ( ( A = B )
| ~ ( B @ singleton @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[66]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(71,plain,
! [A: $i] : ( A @ singleton @ ( A @ member ) ),
inference(simp,[status(thm)],[70]) ).
thf(8,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(54,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,plain,
~ ? [A: $i] : ( empty_set @ ( A @ member ) ),
inference(miniscope,[status(thm)],[54]) ).
thf(56,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(cnf,[status(esa)],[55]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[71,56]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= empty_set )
| ( A != B ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[100]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
<=> ( ( A = C )
| ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair) ).
thf(72,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A = C )
| ( A = B ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) )
& ( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
=> ( ( A = C )
| ( A = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(73,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( A = C )
| ( A = B ) )
=> ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
=> ( ( A = C )
| ( A = B ) ) ) ),
inference(miniscope,[status(thm)],[72]) ).
thf(74,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ unordered_pair ) @ ( D @ member ) )
| ( D != F ) )
& ( ( F @ ( E @ unordered_pair ) @ ( D @ member ) )
| ( D != E ) )
& ( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[73]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(82,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ member ) ),
inference(simp,[status(thm)],[81]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) )
=> ( B @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[18]) ).
thf(20,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk3 ) @ member ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk3 ) @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( empty_set @ ( D @ member ) ) )
| ~ $true
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[21,56]) ).
thf(139,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ member ) )
!= ( empty_set @ ( D @ member ) ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(140,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( empty_set @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( empty_set @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ $true
| ~ ( empty_set @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[82,167]) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ ( empty_set @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(210,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( B @ ( A @ unordered_pair ) @ subset ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ unordered_pair ) )),bind(D,$thf( F ))]]) ).
thf(217,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( B @ ( A @ unordered_pair ) @ subset ) ),
inference(simp,[status(thm)],[210]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( empty_set @ ( A @ ( A @ ( B @ difference ) @ intersection ) @ equal_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI28) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( empty_set @ ( A @ ( A @ ( B @ difference ) @ intersection ) @ equal_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( empty_set @ ( A @ ( A @ ( B @ difference ) @ intersection ) @ equal_set ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
<=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference) ).
thf(57,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) )
=> ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ( ( B @ ( C @ difference ) @ ( A @ member ) )
=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(58,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) )
=> ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ difference ) @ ( A @ member ) )
=> ( ~ ( B @ ( A @ member ) )
& ( C @ ( A @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( F @ difference ) @ ( D @ member ) )
| ( E @ ( D @ member ) )
| ~ ( F @ ( D @ member ) ) )
& ( ~ ( B @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) )
& ( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[71,167]) ).
thf(206,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(207,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ subset ) ),
inference(pattern_uni,[status(thm)],[206:[bind(A,$thf( D )),bind(B,$thf( D @ singleton )),bind(C,$thf( D ))]]) ).
thf(220,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ subset ) ),
inference(simp,[status(thm)],[207]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
<=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) )
=> ( B @ product @ ( A @ member ) ) )
& ( ( B @ product @ ( A @ member ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(91,plain,
( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) )
=> ( B @ product @ ( A @ member ) ) )
& ! [A: $i,B: $i] :
( ( B @ product @ ( A @ member ) )
=> ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( C @ ( A @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[90]) ).
thf(92,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ product @ ( D @ member ) )
| ~ ( D @ ( E @ sk5 ) @ ( D @ member ) ) )
& ( ( E @ product @ ( D @ member ) )
| ( E @ ( D @ ( E @ sk5 ) @ member ) ) )
& ( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ product @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ product @ ( A @ member ) )
| ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[92]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B @ product @ ( A @ member ) )
| ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk5 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ product @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[96,56]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk5 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ product @ ( A @ member ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(329,plain,
! [A: $i] : ( empty_set @ product @ ( A @ member ) ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( E )),bind(B,$thf( empty_set )),bind(C,$thf( E @ ( empty_set @ sk5 ) ))]]) ).
thf(361,plain,
! [A: $i] : ( empty_set @ product @ ( A @ member ) ),
inference(simp,[status(thm)],[329]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(80,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ member ) ),
inference(simp,[status(thm)],[79]) ).
thf(118,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ $true
| ~ ( D @ ( E @ difference ) @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[80,61]) ).
thf(119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ ( D @ ( E @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ unordered_pair ) @ ( A @ difference ) @ ( B @ member ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ unordered_pair ) ))]]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ unordered_pair ) @ ( A @ difference ) @ ( B @ member ) ),
inference(simp,[status(thm)],[120]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_set) ).
thf(26,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ equal_set ) ) )
& ( ( B @ ( A @ equal_set ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[23]) ).
thf(279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk3 ) @ member ) )
!= ( D @ ( C @ ( D @ sk3 ) @ member ) ) )
| ( D @ ( C @ subset ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24,25]) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk3 ) @ member ) )
!= ( D @ ( C @ ( D @ sk3 ) @ member ) ) )
| ( D @ ( C @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[279]) ).
thf(281,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ( A @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[280:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(288,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[281]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union) ).
thf(46,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) )
=> ( C @ ( B @ union ) @ ( A @ member ) ) )
& ( ( C @ ( B @ union ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
| ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( A = B )
| ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[74]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A = C )
| ( A = B ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(27,plain,
( ! [A: $i,B: $i] :
( ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( B @ ( A @ equal_set ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ equal_set ) )
=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ) ),
inference(miniscope,[status(thm)],[26]) ).
thf(28,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ equal_set ) )
| ~ ( C @ ( D @ subset ) )
| ~ ( D @ ( C @ subset ) ) )
& ( ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) )
& ( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(cnfConj,[status(thm)],[28]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ power_set @ ( A @ member ) )
<=> ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',power_set) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ subset ) )
=> ( B @ power_set @ ( A @ member ) ) )
& ( ( B @ power_set @ ( A @ member ) )
=> ( B @ ( A @ subset ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,56]) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( A != C ) ),
inference(simp,[status(thm)],[115]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[121]) ).
thf(15,plain,
( ~ ( empty_set @ ( sk1 @ ( sk1 @ ( sk2 @ difference ) @ intersection ) @ equal_set ) )
& ( sk2 @ ( sk1 @ subset ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
sk2 @ ( sk1 @ subset ),
inference(cnfConj,[status(thm)],[15]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( empty_set @ ( A @ subset ) ) )
| ~ ( A @ ( B @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,167]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ subset ) )
!= ( empty_set @ ( A @ subset ) ) )
| ~ ( A @ ( B @ member ) ) ),
inference(simp,[status(thm)],[214]) ).
thf(216,plain,
! [B: $i,A: $i] :
( ( sk2 != empty_set )
| ( sk1 != A )
| ~ ( A @ ( B @ member ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(219,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ~ ( sk1 @ ( A @ member ) ) ),
inference(simp,[status(thm)],[216]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk5 ) @ member ) )
!= ( sk1 @ ( C @ member ) ) )
| ( sk2 != empty_set )
| ~ $true
| ( B @ product @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[96,219]) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk5 ) @ member ) )
!= ( sk1 @ ( C @ member ) ) )
| ( sk2 != empty_set )
| ( B @ product @ ( A @ member ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(347,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( sk1 @ product @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( E )),bind(B,$thf( sk1 )),bind(C,$thf( E @ ( sk1 @ sk5 ) ))]]) ).
thf(362,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( sk1 @ product @ ( A @ member ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ product @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true
| ( sk2 != empty_set ) ),
inference(paramod_ordered,[status(thm)],[362,56]) ).
thf(383,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ product @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[382]) ).
thf(406,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ product )
!= empty_set )
| ( A != B )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[383]) ).
thf(412,plain,
( ( ( sk1 @ product )
!= empty_set )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[406]) ).
thf(17,plain,
~ ( empty_set @ ( sk1 @ ( sk1 @ ( sk2 @ difference ) @ intersection ) @ equal_set ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( C @ ( B @ ( C @ sk3 ) @ member ) ) )
| ( C @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[361,25]) ).
thf(432,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( C @ ( B @ ( C @ sk3 ) @ member ) ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[431]) ).
thf(433,plain,
! [A: $i] : ( empty_set @ product @ ( A @ subset ) ),
inference(pattern_uni,[status(thm)],[432:[bind(A,$thf( E @ ( empty_set @ product @ sk3 ) )),bind(B,$thf( E )),bind(C,$thf( empty_set @ product ))]]) ).
thf(444,plain,
! [A: $i] : ( empty_set @ product @ ( A @ subset ) ),
inference(simp,[status(thm)],[433]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk3 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24,56]) ).
thf(225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk3 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(226,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk3 ) ))]]) ).
thf(245,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[226]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ intersection ) @ ( A @ member ) )
<=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection) ).
thf(39,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) )
=> ( C @ ( B @ intersection ) @ ( A @ member ) ) )
& ( ( C @ ( B @ intersection ) @ ( A @ member ) )
=> ( ( C @ ( A @ member ) )
& ( B @ ( A @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(252,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk3 ) @ member ) )
!= ( sk1 @ ( C @ member ) ) )
| ( sk2 != empty_set )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[24,219]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk3 ) @ member ) )
!= ( sk1 @ ( C @ member ) ) )
| ( sk2 != empty_set )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[252]) ).
thf(254,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( A @ ( sk1 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[253:[bind(A,$thf( sk1 )),bind(B,$thf( D )),bind(C,$thf( sk1 @ ( D @ sk3 ) ))]]) ).
thf(271,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( A @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[254]) ).
thf(417,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[361,56]) ).
thf(418,plain,
! [B: $i,A: $i] :
( ( empty_set @ product @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[417]) ).
thf(443,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ product )
!= empty_set )
| ( A != B ) ),
inference(simp,[status(thm)],[418]) ).
thf(451,plain,
( ( empty_set @ product )
!= empty_set ),
inference(simp,[status(thm)],[443]) ).
thf(221,plain,
! [A: $i] :
( ( ( empty_set @ ( A @ singleton @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16,220]) ).
thf(222,plain,
! [A: $i] :
( ( empty_set @ ( A @ singleton @ subset ) )
!= ( sk2 @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(223,plain,
! [A: $i] :
( ( sk2 != empty_set )
| ( ( A @ singleton )
!= sk1 ) ),
inference(simp,[status(thm)],[222]) ).
thf(436,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[361,167]) ).
thf(437,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[436]) ).
thf(438,plain,
~ ( empty_set @ ( empty_set @ product @ subset ) ),
inference(pattern_uni,[status(thm)],[437:[bind(A,$thf( A )),bind(B,$thf( empty_set @ product )),bind(C,$thf( A ))]]) ).
thf(399,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ product @ ( A @ member ) )
!= ( sk1 @ ( B @ member ) ) )
| ( sk2 != empty_set )
| ~ $true
| ( sk2 != empty_set ) ),
inference(paramod_ordered,[status(thm)],[362,219]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ product @ ( A @ member ) )
!= ( sk1 @ ( B @ member ) ) )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[399]) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ product )
!= sk1 )
| ( A != B )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[400]) ).
thf(414,plain,
( ( ( sk1 @ product )
!= sk1 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[407]) ).
thf(104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( C @ ( B @ member ) ) )
| ~ $true
| ~ ( C @ ( D @ difference ) @ ( B @ member ) ) ),
inference(paramod_ordered,[status(thm)],[71,61]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( C @ ( B @ member ) ) )
| ~ ( C @ ( D @ difference ) @ ( B @ member ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
! [B: $i,A: $i] :
~ ( B @ singleton @ ( A @ difference ) @ ( B @ member ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ singleton ))]]) ).
thf(111,plain,
! [B: $i,A: $i] :
~ ( B @ singleton @ ( A @ difference ) @ ( B @ member ) ),
inference(simp,[status(thm)],[106]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( C @ singleton @ ( B @ difference ) @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[71,111]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( C @ singleton @ ( B @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(179,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton )
!= ( C @ singleton @ ( B @ difference ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[174]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ difference ) )
!= ( B @ singleton ) ),
inference(simp,[status(thm)],[179]) ).
thf(126,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,56]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( B != C ) ),
inference(simp,[status(thm)],[127]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[133]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( sk1 @ ( C @ member ) ) )
| ( sk2 != empty_set )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[82,219]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( sk1 @ ( C @ member ) ) )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[260]) ).
thf(264,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk1 )
| ( B != C )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[261]) ).
thf(268,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk1 )
| ( sk2 != empty_set ) ),
inference(simp,[status(thm)],[264]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ sum @ ( A @ member ) )
<=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sum) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) )
=> ( B @ sum @ ( A @ member ) ) )
& ( ( B @ sum @ ( A @ member ) )
=> ? [C: $i] :
( ( C @ ( A @ member ) )
& ( B @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2475,plain,
$false,
inference(e,[status(thm)],[101,217,56,14,61,220,361,123,72,26,82,24,288,25,46,57,78,29,21,33,124,96,412,64,17,444,71,54,219,245,39,271,362,451,223,438,80,167,18,414,182,16,136,268,83,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET696+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.37 % Computer : n011.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 08:05:44 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.26/1.19 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.89/1.51 % [INFO] Parsing done (314ms).
% 1.89/1.54 % [INFO] Running in sequential loop mode.
% 3.10/2.22 % [INFO] eprover registered as external prover.
% 3.10/2.23 % [INFO] Scanning for conjecture ...
% 3.29/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 3.49/2.42 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 3.49/2.45 % [INFO] Problem is first-order (TPTP FOF).
% 3.49/2.46 % [INFO] Type checking passed.
% 3.49/2.47 % [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 ...
% 18.84/5.78 % External prover 'e' found a proof!
% 18.84/5.78 % [INFO] Killing All external provers ...
% 18.84/5.79 % Time passed: 5271ms (effective reasoning time: 4239ms)
% 18.84/5.79 % 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)>
% 18.84/5.79 % Axioms used in derivation (11): power_set, unordered_pair, union, intersection, empty_set, subset, equal_set, singleton, difference, sum, product
% 18.84/5.79 % No. of inferences in proof: 149
% 18.84/5.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5271 ms resp. 4239 ms w/o parsing
% 17.70/5.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.70/5.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------