%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET351+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 : n026.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 08:29:59 AM UTC 2026
% Result : Theorem 23.32s 5.09s
% Output : Refutation 20.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 15
% Syntax : Number of formulae : 156 ( 58 unt; 0 typ; 3 def)
% Number of atoms : 467 ( 108 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 1423 ( 191 ~; 115 |; 43 &;1020 @)
% ( 10 <=>; 44 =>; 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 : 18 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 431 ( 4 ^; 420 !; 4 ?; 431 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(equal_set_decl,type,
equal_set: $i > $i > $o ).
thf(sum_decl,type,
sum: $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(power_set_decl,type,
power_set: $i > $i ).
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(union_decl,type,
union: $i > $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(difference_decl,type,
difference: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(product_decl,type,
product: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( A @ ( A @ singleton @ sum @ equal_set ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [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(62,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(63,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)],[62]) ).
thf(64,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)],[63]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[64]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[66]) ).
thf(69,plain,
! [A: $i] : ( A @ singleton @ ( A @ member ) ),
inference(simp,[status(thm)],[68]) ).
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(55,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(56,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)],[55]) ).
thf(57,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)],[56]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ member ) )
| ~ ( B @ ( C @ difference ) @ ( A @ member ) ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(102,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)],[69,59]) ).
thf(103,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)],[102]) ).
thf(104,plain,
! [B: $i,A: $i] :
~ ( B @ singleton @ ( A @ difference ) @ ( B @ member ) ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ singleton ))]]) ).
thf(109,plain,
! [B: $i,A: $i] :
~ ( B @ singleton @ ( A @ difference ) @ ( B @ member ) ),
inference(simp,[status(thm)],[104]) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( C @ singleton @ ( B @ difference ) @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,109]) ).
thf(113,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( C @ singleton @ ( B @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton )
!= ( C @ singleton @ ( B @ difference ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[113]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ difference ) )
!= ( B @ singleton ) ),
inference(simp,[status(thm)],[114]) ).
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(70,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(71,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)],[70]) ).
thf(72,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)],[71]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[74]) ).
thf(78,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ member ) ),
inference(simp,[status(thm)],[77]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(79,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ member ) )
| ( A != C ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(80,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ member ) ),
inference(simp,[status(thm)],[79]) ).
thf(8,axiom,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',empty_set) ).
thf(52,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(53,plain,
~ ? [A: $i] : ( empty_set @ ( A @ member ) ),
inference(miniscope,[status(thm)],[52]) ).
thf(54,plain,
! [A: $i] :
~ ( empty_set @ ( A @ member ) ),
inference(cnf,[status(esa)],[53]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,54]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( B != C ) ),
inference(simp,[status(thm)],[140]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[143]) ).
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(88,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(89,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)],[88]) ).
thf(90,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ product @ ( D @ member ) )
| ~ ( D @ ( E @ sk4 ) @ ( D @ member ) ) )
& ( ( E @ product @ ( D @ member ) )
| ( E @ ( D @ ( E @ sk4 ) @ member ) ) )
& ( ( C @ ( A @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( B @ product @ ( A @ member ) ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ product @ ( A @ member ) )
| ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[90]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ product @ ( A @ member ) )
| ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk4 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ product @ ( A @ member ) ) ),
inference(paramod_ordered,[status(thm)],[94,54]) ).
thf(330,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ sk4 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ product @ ( A @ member ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(331,plain,
! [A: $i] : ( empty_set @ product @ ( A @ member ) ),
inference(pattern_uni,[status(thm)],[330:[bind(A,$thf( E )),bind(B,$thf( empty_set )),bind(C,$thf( E @ ( empty_set @ sk4 ) ))]]) ).
thf(347,plain,
! [A: $i] : ( empty_set @ product @ ( A @ member ) ),
inference(simp,[status(thm)],[331]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( C @ singleton @ ( B @ difference ) @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,109]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( empty_set @ product @ ( A @ member ) )
!= ( C @ singleton @ ( B @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(373,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ singleton @ ( B @ difference ) )
!= ( empty_set @ product ) )
| ( A != C ) ),
inference(simp,[status(thm)],[359]) ).
thf(380,plain,
! [B: $i,A: $i] :
( ( B @ singleton @ ( A @ difference ) )
!= ( empty_set @ product ) ),
inference(simp,[status(thm)],[373]) ).
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(24,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(25,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)],[24]) ).
thf(26,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)],[25]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(cnfConj,[status(thm)],[26]) ).
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(16,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(17,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)],[16]) ).
thf(18,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk2 ) @ member ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk2 ) @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[17]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(163,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)],[19,54]) ).
thf(164,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)],[163]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( empty_set @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( A )),bind(B,$thf( empty_set )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(173,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ member ) )
| ~ ( empty_set @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(360,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)],[347,173]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(362,plain,
~ ( empty_set @ ( empty_set @ product @ subset ) ),
inference(pattern_uni,[status(thm)],[361:[bind(A,$thf( A )),bind(B,$thf( empty_set @ product )),bind(C,$thf( A ))]]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ product @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_set ) ) ),
inference(paramod_ordered,[status(thm)],[27,362]) ).
thf(402,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( empty_set @ product @ subset ) ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(simp,[status(thm)],[401]) ).
thf(403,plain,
~ ( empty_set @ ( empty_set @ product @ equal_set ) ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( empty_set @ product )),bind(B,$thf( empty_set ))]]) ).
thf(120,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)],[78,59]) ).
thf(121,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)],[120]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ unordered_pair ) @ ( A @ difference ) @ ( B @ member ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ unordered_pair ) ))]]) ).
thf(128,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ unordered_pair ) @ ( A @ difference ) @ ( B @ member ) ),
inference(simp,[status(thm)],[122]) ).
thf(136,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ $true
| ~ ( D @ ( E @ difference ) @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[80,59]) ).
thf(137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( D @ ( C @ member ) ) )
| ~ ( D @ ( E @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ unordered_pair ) @ ( A @ difference ) @ ( C @ member ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ unordered_pair ) ))]]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
~ ( C @ ( B @ unordered_pair ) @ ( A @ difference ) @ ( C @ member ) ),
inference(simp,[status(thm)],[138]) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( D @ ( C @ unordered_pair ) @ ( B @ difference ) @ ( D @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,144]) ).
thf(292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( D @ ( C @ unordered_pair ) @ ( B @ difference ) @ ( D @ member ) ) ),
inference(simp,[status(thm)],[291]) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton )
!= ( D @ ( C @ unordered_pair ) @ ( B @ difference ) ) )
| ( A != D ) ),
inference(simp,[status(thm)],[292]) ).
thf(310,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ difference ) )
!= ( C @ singleton ) ),
inference(simp,[status(thm)],[303]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,54]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( ( A @ singleton )
!= empty_set )
| ( A != B ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(simp,[status(thm)],[98]) ).
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(37,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(1,conjecture,
! [A: $i] : ( A @ ( A @ singleton @ sum @ equal_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI39) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( A @ ( A @ singleton @ sum @ equal_set ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ! [A: $i] : ( A @ ( A @ singleton @ sum @ equal_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( D @ ( C @ unordered_pair ) @ ( B @ difference ) @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[69,128]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ singleton @ ( A @ member ) )
!= ( D @ ( C @ unordered_pair ) @ ( B @ difference ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ singleton )
!= ( D @ ( C @ unordered_pair ) @ ( B @ difference ) ) )
| ( A != C ) ),
inference(simp,[status(thm)],[181]) ).
thf(193,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ difference ) )
!= ( B @ singleton ) ),
inference(simp,[status(thm)],[189]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( D @ singleton @ ( C @ difference ) @ ( D @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,109]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( D @ singleton @ ( C @ difference ) @ ( D @ member ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ singleton @ ( C @ difference ) ) )
| ( A != D ) ),
inference(simp,[status(thm)],[117]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ unordered_pair ) )
!= ( C @ singleton @ ( B @ difference ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk2 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk2 ) @ member ) ) ),
inference(simp,[status(thm)],[20]) ).
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(44,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(215,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk2 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[22,54]) ).
thf(216,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk2 ) @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(217,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(pattern_uni,[status(thm)],[216:[bind(A,$thf( empty_set )),bind(B,$thf( D )),bind(C,$thf( empty_set @ ( D @ sk2 ) ))]]) ).
thf(236,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(simp,[status(thm)],[217]) ).
thf(368,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,54]) ).
thf(369,plain,
! [B: $i,A: $i] :
( ( empty_set @ product @ ( A @ member ) )
!= ( empty_set @ ( B @ member ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(375,plain,
! [B: $i,A: $i] :
( ( ( empty_set @ product )
!= empty_set )
| ( A != B ) ),
inference(simp,[status(thm)],[369]) ).
thf(382,plain,
( ( empty_set @ product )
!= empty_set ),
inference(simp,[status(thm)],[375]) ).
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(81,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(21,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk2 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk2 ) @ member ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(352,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( C @ ( B @ ( C @ sk2 ) @ member ) ) )
| ( C @ ( B @ subset ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[347,23]) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( ( empty_set @ product @ ( A @ member ) )
!= ( C @ ( B @ ( C @ sk2 ) @ member ) ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[352]) ).
thf(354,plain,
! [A: $i] : ( empty_set @ product @ ( A @ subset ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( E @ ( empty_set @ product @ sk2 ) )),bind(B,$thf( E )),bind(C,$thf( empty_set @ product ))]]) ).
thf(377,plain,
! [A: $i] : ( empty_set @ product @ ( A @ subset ) ),
inference(simp,[status(thm)],[354]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk2 ) @ member ) )
!= ( D @ ( C @ ( D @ sk2 ) @ member ) ) )
| ( D @ ( C @ subset ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[22,23]) ).
thf(265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk2 ) @ member ) )
!= ( D @ ( C @ ( D @ sk2 ) @ member ) ) )
| ( D @ ( C @ subset ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[264]) ).
thf(266,plain,
! [A: $i] :
( ( A @ ( A @ subset ) )
| ( A @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[265:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(271,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[266]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ $true
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[69,173]) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ singleton @ ( A @ member ) )
!= ( B @ ( C @ member ) ) )
| ~ ( empty_set @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(198,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ subset ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( D )),bind(B,$thf( D @ singleton )),bind(C,$thf( D ))]]) ).
thf(208,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ subset ) ),
inference(simp,[status(thm)],[198]) ).
thf(391,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( C @ singleton @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_set ) ) ),
inference(paramod_ordered,[status(thm)],[27,208]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( C @ singleton @ subset ) ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(simp,[status(thm)],[391]) ).
thf(393,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ equal_set ) ),
inference(pattern_uni,[status(thm)],[392:[bind(A,$thf( D @ singleton )),bind(B,$thf( empty_set )),bind(C,$thf( D ))]]) ).
thf(399,plain,
! [A: $i] :
~ ( empty_set @ ( A @ singleton @ equal_set ) ),
inference(simp,[status(thm)],[393]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ $true
| ~ ( empty_set @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[78,173]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( C @ ( D @ member ) ) )
| ~ ( empty_set @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( B @ ( A @ unordered_pair ) @ subset ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ unordered_pair ) )),bind(D,$thf( E ))]]) ).
thf(209,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( B @ ( A @ unordered_pair ) @ subset ) ),
inference(simp,[status(thm)],[201]) ).
thf(132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( D @ singleton @ ( C @ difference ) @ ( D @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[80,109]) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ member ) )
!= ( D @ singleton @ ( C @ difference ) @ ( D @ member ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ singleton @ ( C @ difference ) ) )
| ( B != D ) ),
inference(simp,[status(thm)],[133]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ unordered_pair ) )
!= ( C @ singleton @ ( B @ difference ) ) ),
inference(simp,[status(thm)],[141]) ).
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(31,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(394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( D @ ( C @ unordered_pair ) @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ equal_set ) ) ),
inference(paramod_ordered,[status(thm)],[27,209]) ).
thf(395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( empty_set @ ( D @ ( C @ unordered_pair ) @ subset ) ) )
| ~ ( B @ ( A @ equal_set ) ) ),
inference(simp,[status(thm)],[394]) ).
thf(396,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( B @ ( A @ unordered_pair ) @ equal_set ) ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( F @ ( E @ unordered_pair ) )),bind(B,$thf( empty_set )),bind(C,$thf( E )),bind(D,$thf( F ))]]) ).
thf(400,plain,
! [B: $i,A: $i] :
~ ( empty_set @ ( B @ ( A @ unordered_pair ) @ equal_set ) ),
inference(simp,[status(thm)],[396]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[78,54]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ member ) )
!= ( empty_set @ ( C @ member ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( A != C ) ),
inference(simp,[status(thm)],[124]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[127]) ).
thf(15,plain,
~ ( sk1 @ ( sk1 @ singleton @ sum @ equal_set ) ),
inference(cnf,[status(esa)],[14]) ).
thf(6107,plain,
$false,
inference(e,[status(thm)],[115,78,147,380,70,403,128,310,99,19,69,347,88,24,37,52,14,109,193,173,129,22,44,59,27,144,236,382,54,81,377,362,271,208,399,80,209,145,16,31,55,23,400,94,131,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET351+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n026.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 07:36:57 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.71/0.71 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.93/0.82 % [INFO] Parsing done (99ms).
% 0.93/0.82 % [INFO] Running in sequential loop mode.
% 1.19/1.01 % [INFO] eprover registered as external prover.
% 1.19/1.01 % [INFO] Scanning for conjecture ...
% 1.51/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.51/1.07 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.51/1.09 % [INFO] Problem is first-order (TPTP FOF).
% 1.51/1.09 % [INFO] Type checking passed.
% 1.51/1.10 % [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 ...
% 23.32/5.08 % External prover 'e' found a proof!
% 23.32/5.09 % [INFO] Killing All external provers ...
% 23.32/5.09 % Time passed: 4578ms (effective reasoning time: 4262ms)
% 23.32/5.09 % 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)>
% 23.32/5.09 % Axioms used in derivation (11): power_set, unordered_pair, union, intersection, empty_set, subset, equal_set, singleton, difference, sum, product
% 23.32/5.09 % No. of inferences in proof: 153
% 23.32/5.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 4578 ms resp. 4262 ms w/o parsing
% 20.62/5.21 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 20.62/5.21 % [INFO] Killing All external provers ...
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