%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU146+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 : n020.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 10.13s 4.05s
% Output : Refutation 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 73
% Syntax : Number of formulae : 226 ( 95 unt; 0 typ; 12 def)
% Number of atoms : 637 ( 260 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 1605 ( 186 ~; 133 |; 110 &;1036 @)
% ( 22 <=>; 118 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 10 con; 0-3 aty)
% Number of variables : 438 ( 13 ^; 392 !; 21 ?; 438 :)
% ( 0 !>; 0 ?*; 0 @-; 12 @+)
% 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(empty_decl,type,
empty: $i > $o ).
thf(set_union2_decl,type,
set_union2: $i > $i > $i ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(proper_subset_decl,type,
proper_subset: $i > $i > $o ).
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(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i > $o ).
thf(sk10_decl,type,
sk10: $i > $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i > $i ).
thf(sk25_decl,type,
sk25: $i > $i > $i ).
thf(sk26_decl,type,
sk26: $i > $i > $i ).
thf(sk27_decl,type,
sk27: $i > $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(sk6_def,definition,
( sk6
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ set_intersection2 ) @ ( C @ in ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk25_def,definition,
( sk25
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ in ) )
=> ( C = B ) ) ) ) ).
thf(sk26_def,definition,
( sk26
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( C = B )
=> ( A @ ( C @ in ) ) ) ) ) ).
thf(sk27_def,definition,
( sk27
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ in ) ) ) ) ).
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(63,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(64,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)],[63]) ).
thf(65,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)],[64]) ).
thf(67,plain,
( ( sk4
= ( sk5 @ singleton ) )
| ( sk4 = empty_set )
| sk1 ),
inference(cnfConj,[status(thm)],[65]) ).
thf(72,plain,
( sk1
| ( ( sk5 @ singleton )
= sk4 )
| ( sk4 = empty_set ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(70,plain,
( ~ ( sk5 @ singleton @ ( sk4 @ subset ) )
| sk1 ),
inference(cnfConj,[status(thm)],[65]) ).
thf(428,plain,
( ( ( sk5 @ singleton )
!= ( sk5 @ singleton ) )
| ~ ( sk4 @ ( sk4 @ subset ) )
| sk1
| sk1
| ( sk4 = empty_set ) ),
inference(paramod_ordered,[status(thm)],[72,70]) ).
thf(429,plain,
( ( ( sk5 @ singleton )
!= ( sk5 @ singleton ) )
| ~ ( sk4 @ ( sk4 @ subset ) )
| sk1
| ( sk4 = empty_set ) ),
inference(simp,[status(thm)],[428]) ).
thf(430,plain,
( ~ ( sk4 @ ( sk4 @ subset ) )
| sk1
| ( sk4 = empty_set ) ),
inference(pattern_uni,[status(thm)],[429:[]]) ).
thf(34,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).
thf(284,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)],[34]) ).
thf(285,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)],[284]) ).
thf(286,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)],[285]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[286]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[287]) ).
thf(291,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[290]) ).
thf(621,plain,
( ~ $true
| sk1
| ( sk4 = empty_set ) ),
inference(rewrite,[status(thm)],[430,291]) ).
thf(622,plain,
( sk1
| ( sk4 = empty_set ) ),
inference(simp,[status(thm)],[621]) ).
thf(44,axiom,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_xboole_1) ).
thf(326,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(327,plain,
! [A: $i] : ( A @ ( empty_set @ subset ) ),
inference(cnf,[status(esa)],[326]) ).
thf(433,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| ~ $true
| sk1 ),
inference(paramod_ordered,[status(thm)],[327,70]) ).
thf(434,plain,
! [A: $i] :
( ( ( A @ ( empty_set @ subset ) )
!= ( sk5 @ singleton @ ( sk4 @ subset ) ) )
| sk1 ),
inference(simp,[status(thm)],[433]) ).
thf(435,plain,
! [A: $i] :
( ( A
!= ( sk5 @ singleton ) )
| ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[434]) ).
thf(436,plain,
( ( sk4 != empty_set )
| sk1 ),
inference(simp,[status(thm)],[435]) ).
thf(643,plain,
( ( sk4 != sk4 )
| ( empty_set != empty_set )
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[622,436]) ).
thf(644,plain,
( ( sk4 != sk4 )
| sk1 ),
inference(simp,[status(thm)],[643]) ).
thf(645,plain,
sk1,
inference(pattern_uni,[status(thm)],[644:[]]) ).
thf(53,axiom,
! [A: $i] :
( ( A = empty_set )
<=> ! [B: $i] :
~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).
thf(379,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)],[53]) ).
thf(380,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)],[379]) ).
thf(381,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C = empty_set )
| ( C @ ( C @ sk27 @ in ) ) )
& ( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ) ),
inference(cnf,[status(esa)],[380]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(cnfConj,[status(thm)],[381]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ( A != empty_set ) ),
inference(lifteq,[status(thm)],[382]) ).
thf(385,plain,
! [A: $i] :
~ ( empty_set @ ( A @ in ) ),
inference(simp,[status(thm)],[384]) ).
thf(62,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_boole) ).
thf(417,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(157,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(30,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_boole) ).
thf(268,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(269,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[268]) ).
thf(270,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[269]) ).
thf(46,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(331,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)],[46]) ).
thf(20,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(203,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ proper_subset ) )
=> ~ ( A @ ( B @ proper_subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(55,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(390,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)],[55]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ proper_subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',irreflexivity_r2_xboole_0) ).
thf(200,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(33,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(276,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)],[33]) ).
thf(38,axiom,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
thf(308,plain,
! [A: $i] :
( ( A @ empty )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(68,plain,
( ~ sk1
| ( sk2
!= ( sk3 @ singleton ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(73,plain,
( ~ sk1
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(654,plain,
( ~ $true
| ( ( sk3 @ singleton )
!= sk2 ) ),
inference(rewrite,[status(thm)],[73,645]) ).
thf(655,plain,
( ( sk3 @ singleton )
!= sk2 ),
inference(simp,[status(thm)],[654]) ).
thf(201,plain,
~ ? [A: $i] : ( A @ ( A @ proper_subset ) ),
inference(miniscope,[status(thm)],[200]) ).
thf(202,plain,
! [A: $i] :
~ ( A @ ( A @ proper_subset ) ),
inference(cnf,[status(esa)],[201]) ).
thf(58,axiom,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_zfmisc_1) ).
thf(405,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(406,plain,
~ ? [A: $i] :
( ( A @ singleton )
= empty_set ),
inference(miniscope,[status(thm)],[405]) ).
thf(407,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(cnf,[status(esa)],[406]) ).
thf(408,plain,
! [A: $i] :
( ( A @ singleton )
!= empty_set ),
inference(lifteq,[status(thm)],[407]) ).
thf(17,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(170,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) )
= ( B @ ( A @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(152,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ singleton @ subset ) )
<=> ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_zfmisc_1) ).
thf(316,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)],[41]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(78,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(52,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(376,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)],[52]) ).
thf(8,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(92,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)],[8]) ).
thf(93,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)],[92]) ).
thf(94,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 @ sk11 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk9 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk11 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk11 ) ) )
= F )
| ( H @ ( G @ ( F @ sk9 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk9 ) ) )
| ( ( F @ ( G @ ( H @ sk10 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk9 ) ) )
| ( ( F @ ( G @ ( H @ sk10 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk9 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk10 ) ) @ 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)],[93]) ).
thf(102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[102]) ).
thf(106,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[105]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
thf(119,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(120,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [A: $i] :
( ( A @ ( A @ set_union2 ) )
= A ),
inference(lifteq,[status(thm)],[120]) ).
thf(24,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(221,plain,
! [A: $i,B: $i] :
( ( B @ ( B @ ( A @ set_union2 ) @ set_difference ) )
= ( B @ ( A @ set_difference ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(89,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(29,axiom,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t60_xboole_1) ).
thf(265,plain,
! [A: $i,B: $i] :
~ ( ( A @ ( B @ proper_subset ) )
& ( B @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
thf(74,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( A != B )
& ( A @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(15,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(160,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)],[15]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_xboole_1) ).
thf(297,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_intersection2 ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(43,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(324,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ disjoint ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
<=> ( ( B @ ( A @ set_difference ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t83_xboole_1) ).
thf(224,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)],[25]) ).
thf(57,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(403,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)],[57]) ).
thf(54,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(388,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)],[54]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_boole) ).
thf(328,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(47,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(339,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)],[47]) ).
thf(75,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ( B @ empty )
& ( A != B ) )
& ( A @ empty ) ),
inference(miniscope,[status(thm)],[74]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ( A = B )
| ~ ( A @ empty ) ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( B @ empty )
| ~ ( A @ empty )
| ( A = B ) ),
inference(lifteq,[status(thm)],[76]) ).
thf(18,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(173,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)],[18]) ).
thf(50,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t36_xboole_1) ).
thf(371,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_difference ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( empty_set @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[106,385]) ).
thf(784,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( empty_set @ ( C @ in ) ) ),
inference(simp,[status(thm)],[783]) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= empty_set )
| ( B != C ) ),
inference(simp,[status(thm)],[784]) ).
thf(792,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= empty_set ),
inference(simp,[status(thm)],[789]) ).
thf(49,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(350,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)],[49]) ).
thf(351,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)],[350]) ).
thf(352,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk26 ) @ in ) )
| ( ( E @ ( F @ sk25 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk26 ) )
= E )
| ( ( E @ ( F @ sk25 ) )
!= E ) )
& ( ( F
= ( E @ singleton ) )
| ~ ( F @ ( E @ ( F @ sk26 ) @ in ) )
| ( F @ ( E @ ( F @ sk25 ) @ in ) ) )
& ( ( F
= ( E @ singleton ) )
| ( ( E @ ( F @ sk26 ) )
= E )
| ( F @ ( E @ ( F @ sk25 ) @ in ) ) )
& ( ( B @ ( D @ in ) )
| ( D != A )
| ( B
!= ( A @ singleton ) ) )
& ( ( C = A )
| ~ ( B @ ( C @ in ) )
| ( B
!= ( A @ singleton ) ) ) ),
inference(cnf,[status(esa)],[351]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(cnfConj,[status(thm)],[352]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ in ) )
| ( C != A )
| ( B
!= ( A @ singleton ) ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(360,plain,
! [A: $i] : ( A @ singleton @ ( A @ in ) ),
inference(simp,[status(thm)],[359]) ).
thf(21,axiom,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
thf(205,plain,
! [A: $i,B: $i] :
~ ( ( B @ empty )
& ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(39,axiom,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_boole) ).
thf(311,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(69,plain,
( ~ sk1
| ( sk2 != empty_set ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(71,plain,
( ~ sk1
| ( sk2 != empty_set ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(656,plain,
( ~ $true
| ( sk2 != empty_set ) ),
inference(rewrite,[status(thm)],[71,645]) ).
thf(657,plain,
sk2 != empty_set,
inference(simp,[status(thm)],[656]) ).
thf(60,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_xboole_1) ).
thf(412,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ set_intersection2 ) @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(35,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(296,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(90,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[89]) ).
thf(91,plain,
~ ( sk8 @ empty ),
inference(cnf,[status(esa)],[90]) ).
thf(423,plain,
( ( ( sk8 @ empty )
!= ( empty_set @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[296,91]) ).
thf(424,plain,
( ( sk8 @ empty )
!= ( empty_set @ empty ) ),
inference(simp,[status(thm)],[423]) ).
thf(425,plain,
sk8 != empty_set,
inference(simp,[status(thm)],[424]) ).
thf(11,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(149,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(312,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(cnf,[status(esa)],[311]) ).
thf(313,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_difference ) )
= A ),
inference(lifteq,[status(thm)],[312]) ).
thf(6,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(83,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)],[6]) ).
thf(84,plain,
( ~ ? [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
& ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) ) )
& ~ ? [A: $i,B: $i] :
( ~ ? [C: $i] : ( B @ ( A @ set_intersection2 ) @ ( C @ in ) )
& ~ ( B @ ( A @ disjoint ) ) ) ),
inference(miniscope,[status(thm)],[83]) ).
thf(85,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( D @ ( C @ disjoint ) )
| ~ ( D @ ( C @ set_intersection2 ) @ ( E @ in ) ) )
& ( ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk7 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ) ),
inference(cnf,[status(esa)],[84]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk7 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ),
inference(cnfConj,[status(thm)],[85]) ).
thf(158,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(cnf,[status(esa)],[157]) ).
thf(159,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(lifteq,[status(thm)],[158]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(219,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(32,axiom,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).
thf(274,plain,
! [A: $i,B: $i] : ( B @ ( A @ set_union2 ) @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(418,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(cnf,[status(esa)],[417]) ).
thf(419,plain,
! [A: $i] :
( ( empty_set @ ( A @ set_intersection2 ) )
= empty_set ),
inference(lifteq,[status(thm)],[418]) ).
thf(31,axiom,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_xboole_1) ).
thf(271,plain,
! [A: $i] :
( ( empty_set @ ( A @ subset ) )
=> ( A = empty_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,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(208,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)],[22]) ).
thf(329,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(cnf,[status(esa)],[328]) ).
thf(330,plain,
! [A: $i] :
( ( A @ ( empty_set @ set_difference ) )
= empty_set ),
inference(lifteq,[status(thm)],[329]) ).
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(80,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( A @ ( B @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(167,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[94]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[98]) ).
thf(112,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[111]) ).
thf(48,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(342,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)],[48]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
thf(414,plain,
! [A: $i] :
( ( A @ ( A @ unordered_pair ) )
= ( A @ singleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
thf(409,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( ( B @ ( A @ set_union2 ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(13,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(154,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_difference ) @ ( A @ set_difference ) )
= ( B @ ( A @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(40,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(314,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) )
=> ( C @ ( A @ subset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(27,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(235,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)],[27]) ).
thf(81,plain,
! [A: $i] :
( ~ ( A @ empty )
=> ~ ? [B: $i] : ( A @ ( B @ set_union2 ) @ empty ) ),
inference(miniscope,[status(thm)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ set_union2 ) @ empty )
| ( A @ empty ) ),
inference(cnf,[status(esa)],[81]) ).
thf(37,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(300,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)],[37]) ).
thf(28,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(262,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_union2 ) )
= ( A @ ( B @ set_union2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(79,plain,
sk6 @ empty,
inference(cnf,[status(esa)],[78]) ).
thf(420,plain,
( ( ( sk8 @ empty )
!= ( sk6 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,91]) ).
thf(421,plain,
( ( sk8 @ empty )
!= ( sk6 @ empty ) ),
inference(simp,[status(thm)],[420]) ).
thf(422,plain,
sk8 != sk6,
inference(simp,[status(thm)],[421]) ).
thf(51,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(373,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
=> ( B
= ( A @ ( B @ set_difference ) @ ( A @ set_union2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(56,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(400,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)],[56]) ).
thf(42,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(322,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(10,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(122,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)],[10]) ).
thf(66,plain,
( ~ sk1
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ),
inference(cnfConj,[status(thm)],[65]) ).
thf(658,plain,
( ~ $true
| ( sk3 @ singleton @ ( sk2 @ subset ) ) ),
inference(rewrite,[status(thm)],[66,645]) ).
thf(659,plain,
sk3 @ singleton @ ( sk2 @ subset ),
inference(simp,[status(thm)],[658]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_xboole_0) ).
thf(232,plain,
! [A: $i,B: $i] :
( ~ ( A @ empty )
=> ~ ( B @ ( A @ set_union2 ) @ empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1039,plain,
$false,
inference(e,[status(thm)],[645,385,417,157,270,291,331,203,390,200,276,308,379,655,202,408,170,284,152,316,78,376,106,121,221,89,265,74,160,297,92,324,224,403,388,328,339,77,173,371,792,360,205,311,657,412,425,296,149,313,350,86,159,219,274,419,271,208,91,330,80,167,112,342,63,414,327,409,154,314,119,235,82,300,262,405,422,373,326,268,79,400,322,122,83,659,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU146+2 : 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
% 0.13/0.40 % Computer : n020.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 08:41:19 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.48/1.21 % [INFO] Parsing done (219ms).
% 1.48/1.22 % [INFO] Running in sequential loop mode.
% 2.15/1.63 % [INFO] eprover registered as external prover.
% 2.15/1.64 % [INFO] Scanning for conjecture ...
% 2.37/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 66 axioms. Running axiom selection ...
% 2.53/1.84 % [INFO] Axiom selection finished. Selected 60 axioms (removed 6 axioms).
% 2.78/1.92 % [INFO] Problem is first-order (TPTP FOF).
% 2.78/1.94 % [INFO] Type checking passed.
% 2.78/1.94 % [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 ...
% 10.13/4.05 % External prover 'e' found a proof!
% 10.13/4.05 % [INFO] Killing All external provers ...
% 10.13/4.05 % Time passed: 3511ms (effective reasoning time: 2822ms)
% 10.13/4.05 % 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)>
% 10.13/4.05 % Axioms used in derivation (60): fc1_xboole_0, t2_boole, d1_xboole_0, t6_boole, l2_zfmisc_1, t2_xboole_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, d8_xboole_0, t2_tarski, t33_xboole_1, l32_xboole_1, t4_boole, fc3_xboole_0, d2_xboole_0, t7_boole, t48_xboole_1, d7_xboole_0, t83_xboole_1, antisymmetry_r2_xboole_0, l3_zfmisc_1, commutativity_k2_tarski, t69_enumset1, t26_xboole_1, t63_xboole_1, t8_xboole_1, t28_xboole_1, d3_tarski, reflexivity_r1_tarski, d4_xboole_0, t36_xboole_1, t8_boole, rc1_xboole_0, t12_xboole_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
% 10.13/4.05 % No. of inferences in proof: 214
% 10.13/4.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3511 ms resp. 2822 ms w/o parsing
% 9.68/4.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.68/4.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------