%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU146+1 : 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 : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:37:44 AM UTC 2026
% Result : Theorem 9.98s 3.92s
% Output : Refutation 9.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 10
% Syntax : Number of formulae : 93 ( 20 unt; 0 typ; 4 def)
% Number of atoms : 281 ( 100 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 714 ( 108 ~; 111 |; 21 &; 446 @)
% ( 5 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 119 ( 0 ^; 115 !; 0 ?; 119 :)
% ( 0 !>; 0 ?*; 0 @-; 4 @+)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ singleton @ ( sk2 @ subset ) )
=> ( ( sk2
= ( A @ singleton ) )
| ( sk2 = empty_set ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ( ( ( sk4
= ( A @ singleton ) )
| ( sk4 = empty_set ) )
=> ( A @ singleton @ ( sk4 @ subset ) ) ) ) ) ).
thf(15,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(64,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)],[15]) ).
thf(65,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_difference ) )
= empty_set ) )
& ! [A: $i,B: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
=> ( B @ ( A @ subset ) ) ) ),
inference(miniscope,[status(thm)],[64]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ ( C @ set_difference ) )
= empty_set )
| ~ ( D @ ( C @ subset ) ) )
& ( ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
!= empty_set ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
= empty_set )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[66]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ subset ) )
| ( ( B @ ( A @ set_difference ) )
= empty_set ) ),
inference(simp,[status(thm)],[70]) ).
thf(1,conjecture,
! [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(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(17,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)],[2]) ).
thf(18,plain,
~ ( ! [A: $i,B: $i] :
( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(miniscope,[status(thm)],[17]) ).
thf(19,plain,
( ( ~ ( sk5 @ singleton @ ( sk4 @ subset ) )
| sk1 )
& ( ( sk4
= ( sk5 @ singleton ) )
| ( sk4 = empty_set )
| sk1 )
& ( ~ sk1
| ( sk2
!= ( sk3 @ singleton ) ) )
& ( ~ sk1
| ( sk2 != empty_set ) )
& ( ~ sk1
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(23,plain,
( ~ sk1
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(24,plain,
( ( sk4
= ( sk5 @ singleton ) )
| ( sk4 = empty_set )
| sk1 ),
inference(cnfConj,[status(thm)],[19]) ).
thf(25,plain,
( sk1
| ( ( sk5 @ singleton )
= sk4 )
| ( sk4 = empty_set ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(20,plain,
( ~ ( sk5 @ singleton @ ( sk4 @ subset ) )
| sk1 ),
inference(cnfConj,[status(thm)],[19]) ).
thf(82,plain,
( ( ( sk5 @ singleton )
!= ( sk5 @ singleton ) )
| ~ ( sk4 @ ( sk4 @ subset ) )
| sk1
| sk1
| ( sk4 = empty_set ) ),
inference(paramod_ordered,[status(thm)],[25,20]) ).
thf(83,plain,
( ( ( sk5 @ singleton )
!= ( sk5 @ singleton ) )
| ~ ( sk4 @ ( sk4 @ subset ) )
| sk1
| ( sk4 = empty_set ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
( ~ ( sk4 @ ( sk4 @ subset ) )
| sk1
| ( sk4 = empty_set ) ),
inference(pattern_uni,[status(thm)],[83:[]]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(30,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)],[4]) ).
thf(31,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)],[30]) ).
thf(32,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)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(37,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[36]) ).
thf(99,plain,
( ~ $true
| sk1
| ( sk4 = empty_set ) ),
inference(rewrite,[status(thm)],[84,37]) ).
thf(100,plain,
( sk1
| ( sk4 = empty_set ) ),
inference(simp,[status(thm)],[99]) ).
thf(14,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(62,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(63,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[62]) ).
thf(88,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[63,20]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| sk1 ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: $i] :
( ( A
!= ( sk5 @ singleton ) )
| ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
( ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[90]) ).
thf(104,plain,
( ( sk4 != sk4 )
| ( empty_set != empty_set )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[100,91]) ).
thf(105,plain,
( ( sk4 != sk4 )
| sk1 ),
inference(simp,[status(thm)],[104]) ).
thf(106,plain,
sk1,
inference(pattern_uni,[status(thm)],[105:[]]) ).
thf(111,plain,
( ~ $true
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ),
inference(rewrite,[status(thm)],[23,106]) ).
thf(112,plain,
sk3 @ singleton @ ( sk2 @ subset ),
inference(simp,[status(thm)],[111]) ).
thf(10,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(52,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)],[10]) ).
thf(53,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ! [C: $i] :
( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ) ),
inference(miniscope,[status(thm)],[52]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ singleton @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[112,54]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ singleton @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ( C @ singleton @ ( B @ set_difference ) @ ( A @ subset ) )
| ( A @ ( C @ in ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(273,plain,
! [A: $i] :
( ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) )
| ( sk2 @ ( A @ in ) ) ),
inference(pattern_uni,[status(thm)],[272:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 @ singleton )),bind(C,$thf( C ))]]) ).
thf(284,plain,
! [A: $i] :
( ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) )
| ( sk2 @ ( A @ in ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(46,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)],[9]) ).
thf(47,plain,
( ! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ( B @ ( A @ singleton @ subset ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
=> ( B @ ( A @ in ) ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ singleton @ subset ) )
| ~ ( D @ ( C @ in ) ) )
& ( ( B @ ( A @ in ) )
| ~ ( B @ ( A @ singleton @ subset ) ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ singleton @ subset ) )
| ~ ( B @ ( A @ in ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ singleton @ subset ) )
| ~ $true
| ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[284,51]) ).
thf(537,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ in ) )
!= ( C @ ( B @ in ) ) )
| ( C @ ( B @ singleton @ subset ) )
| ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(538,plain,
! [A: $i] :
( ( sk2 @ ( A @ singleton @ subset ) )
| ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk2 ))]]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[32]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[40]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ singleton @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[112,41]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ singleton @ ( sk2 @ subset ) )
!= ( B @ ( A @ subset ) ) )
| ~ ( A @ ( B @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[178]) ).
thf(180,plain,
( ~ ( sk2 @ ( sk3 @ singleton @ subset ) )
| ( ( sk3 @ singleton )
= sk2 ) ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 @ singleton ))]]) ).
thf(22,plain,
( ~ sk1
| ( sk2
!= ( sk3 @ singleton ) ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(27,plain,
( ~ sk1
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(107,plain,
( ~ $true
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(rewrite,[status(thm)],[27,106]) ).
thf(108,plain,
( ( sk3 @ singleton )
!= sk2 ),
inference(simp,[status(thm)],[107]) ).
thf(498,plain,
~ ( sk2 @ ( sk3 @ singleton @ subset ) ),
inference(simplifyReflect,[status(thm)],[180,108]) ).
thf(1004,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ singleton @ subset ) )
!= ( sk2 @ ( sk3 @ singleton @ subset ) ) )
| ~ $true
| ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[538,498]) ).
thf(1005,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ singleton @ subset ) )
!= ( sk2 @ ( sk3 @ singleton @ subset ) ) )
| ( A @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[1004]) ).
thf(1006,plain,
sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ),
inference(pattern_uni,[status(thm)],[1005:[bind(A,$thf( sk3 ))]]) ).
thf(21,plain,
( ~ sk1
| ( sk2 != empty_set ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(26,plain,
( ~ sk1
| ( sk2 != empty_set ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(109,plain,
( ~ $true
| ( sk2 != empty_set ) ),
inference(rewrite,[status(thm)],[26,106]) ).
thf(110,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[109]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != empty_set )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[41,110]) ).
thf(162,plain,
! [A: $i] :
( ( A != empty_set )
| ~ ( sk2 @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( sk2 ))]]) ).
thf(165,plain,
( ~ ( sk2 @ ( empty_set @ subset ) )
| ~ ( empty_set @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(291,plain,
( ~ $true
| ~ ( empty_set @ ( sk2 @ subset ) ) ),
inference(rewrite,[status(thm)],[165,63]) ).
thf(292,plain,
~ ( empty_set @ ( sk2 @ subset ) ),
inference(simp,[status(thm)],[291]) ).
thf(1087,plain,
( ( ( sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) )
!= ( empty_set @ ( sk2 @ subset ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1006,292]) ).
thf(1088,plain,
( ( sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) @ ( sk2 @ subset ) )
!= ( empty_set @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[1087]) ).
thf(1136,plain,
( ( ( sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) )
!= empty_set )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[1088]) ).
thf(1146,plain,
( ( sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) )
!= empty_set ),
inference(simp,[status(thm)],[1136]) ).
thf(1441,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
!= ( sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) ) )
| ( empty_set != empty_set )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[71,1146]) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_difference ) )
!= ( sk3 @ singleton @ ( sk3 @ singleton @ set_difference ) ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[1441]) ).
thf(1443,plain,
~ ( sk3 @ singleton @ ( sk3 @ singleton @ subset ) ),
inference(pattern_uni,[status(thm)],[1442:[bind(A,$thf( sk3 @ singleton )),bind(B,$thf( sk3 @ singleton ))]]) ).
thf(1455,plain,
~ $true,
inference(rewrite,[status(thm)],[1443,37]) ).
thf(1456,plain,
$false,
inference(simp,[status(thm)],[1455]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n017.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 08:35:51 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 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
% 0.87/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.19 % [INFO] Parsing done (188ms).
% 1.40/1.21 % [INFO] Running in sequential loop mode.
% 2.05/1.61 % [INFO] eprover registered as external prover.
% 2.05/1.62 % [INFO] Scanning for conjecture ...
% 2.26/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 14 axioms. Running axiom selection ...
% 2.26/1.76 % [INFO] Axiom selection finished. Selected 14 axioms (removed 0 axioms).
% 2.26/1.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.26/1.79 % [INFO] Type checking passed.
% 2.26/1.79 % [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 ...
% 9.98/3.92 % [INFO] Killing All external provers ...
% 9.98/3.92 % Time passed: 3357ms (effective reasoning time: 2706ms)
% 9.98/3.92 % 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)>
% 9.98/3.92 % Axioms used in derivation (5): t37_xboole_1, l3_zfmisc_1, l2_zfmisc_1, t2_xboole_1, d10_xboole_0
% 9.98/3.92 % No. of inferences in proof: 89
% 9.98/3.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3357 ms resp. 2706 ms w/o parsing
% 9.98/3.99 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.98/3.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------