%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% 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 : n005.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 08:29:34 AM UTC 2026
% Result : Theorem 26.37s 11.91s
% Output : Refutation 26.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 119 ( 24 unt; 0 typ; 6 def)
% Number of atoms : 400 ( 120 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1524 ( 181 ~; 181 |; 33 &;1092 @)
% ( 5 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 302 ( 6 ^; 290 !; 0 ?; 302 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(intersection_decl,type,
intersection: $i > $i > $i ).
thf(member_decl,type,
member: $i > $i > $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ intersection ) @ intersection ) )
= ( C @ ( B @ intersection ) @ ( A @ intersection ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk1 @ intersection ) @ intersection ) )
= ( B @ ( A @ intersection ) @ ( sk1 @ intersection ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) )
!= ( A @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ subset ) )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
thf(34,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)],[6]) ).
thf(35,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)],[34]) ).
thf(36,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk4 ) @ member ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk4 ) @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[38]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
<=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
thf(12,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ( ( B @ ( A @ intersection ) @ ( C @ member ) )
=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
( ! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) )
=> ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
=> ( ( B @ ( C @ member ) )
& ( A @ ( C @ member ) ) ) ) ),
inference(miniscope,[status(thm)],[12]) ).
thf(14,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ intersection ) @ ( F @ member ) )
| ~ ( E @ ( F @ member ) )
| ~ ( D @ ( F @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( D @ ( C @ intersection ) @ ( E @ member ) ) )
| ( C @ ( E @ member ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[40,15]) ).
thf(249,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( D @ ( C @ intersection ) @ ( E @ member ) ) )
| ( C @ ( E @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ intersection ) @ ( A @ sk4 ) @ member ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[249:[bind(A,$thf( I @ ( H @ intersection ) )),bind(B,$thf( F )),bind(C,$thf( H )),bind(D,$thf( I )),bind(E,$thf( I @ ( H @ intersection ) @ ( F @ sk4 ) ))]]) ).
thf(253,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ intersection ) @ ( A @ sk4 ) @ member ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(simp,[status(thm)],[250]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ! [C: $i] :
( ( A @ ( C @ member ) )
<=> ( B @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) )
& ( ( A = B )
=> ! [C: $i] :
( ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ intersection ) @ intersection ) )
= ( C @ ( B @ intersection ) @ ( A @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_intersection) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ intersection ) @ intersection ) )
= ( C @ ( B @ intersection ) @ ( A @ intersection ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ intersection ) @ intersection ) )
= ( C @ ( B @ intersection ) @ ( A @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) )
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) )
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) ) )
| ( ( A @ ( B @ intersection ) )
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,11]) ).
thf(139,plain,
( ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) )
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( sk2 @ ( sk1 @ intersection ) )),bind(B,$thf( sk3 ))]]) ).
thf(155,plain,
( ( ( sk3 @ ( sk2 @ intersection ) )
!= ( sk2 @ ( sk1 @ intersection ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[139]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( D @ ( C @ intersection ) ) )
| ( D @ ( E @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( E @ member ) ) ),
inference(paramod_ordered,[status(thm)],[33,16]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[224]) ).
thf(235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( D @ ( C @ intersection ) @ ( E @ member ) ) )
| ( D @ ( E @ member ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[40,16]) ).
thf(236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( D @ ( C @ intersection ) @ ( E @ member ) ) )
| ( D @ ( E @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ intersection ) @ ( A @ sk4 ) @ member ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[236:[bind(A,$thf( I @ ( H @ intersection ) )),bind(B,$thf( F )),bind(C,$thf( H )),bind(D,$thf( I )),bind(E,$thf( I @ ( H @ intersection ) @ ( F @ sk4 ) ))]]) ).
thf(254,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ intersection ) @ ( A @ sk4 ) @ member ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ intersection ) @ ( A @ sk4 ) @ member ) )
!= ( E @ ( D @ ( E @ sk4 ) @ member ) ) )
| ( E @ ( D @ subset ) )
| ~ $true
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[253,41]) ).
thf(354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( B @ intersection ) @ ( A @ sk4 ) @ member ) )
!= ( E @ ( D @ ( E @ sk4 ) @ member ) ) )
| ( E @ ( D @ subset ) )
| ( A @ ( C @ ( B @ intersection ) @ subset ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ intersection ) @ subset ) )
| ( A @ ( B @ ( A @ intersection ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ intersection ) )),bind(E,$thf( F ))]]) ).
thf(388,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ intersection ) @ subset ) ),
inference(simp,[status(thm)],[355]) ).
thf(445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( D @ ( C @ intersection ) ) )
| ( C @ ( A @ ( B @ intersection ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[33,388]) ).
thf(446,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ intersection ) @ subset ) ),
inference(pattern_uni,[status(thm)],[445:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( C @ ( D @ intersection ) ) )
| ( C @ ( A @ ( B @ intersection ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[33,446]) ).
thf(472,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ intersection ) @ subset ) ),
inference(pattern_uni,[status(thm)],[471:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(645,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ intersection ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[472,37]) ).
thf(646,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ intersection ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) ) ),
inference(simp,[status(thm)],[645]) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[646:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ intersection ) )),bind(D,$thf( F ))]]) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[647]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(42,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(19,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(20,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)],[19]) ).
thf(21,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)],[20]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[29]) ).
thf(186,plain,
( ( sk3 != sk2 )
| ( sk2 != sk1 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[155]) ).
thf(273,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( sk3 != sk2 )
| ( B != sk1 )
| ( sk3 != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[30,186]) ).
thf(274,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( A != sk1 )
| ( sk3 != sk1 )
| ~ ( sk2 @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( sk2 ))]]) ).
thf(284,plain,
( ( sk3 != sk2 )
| ( sk3 != sk1 )
| ~ ( sk2 @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ intersection ) )
!= ( D @ ( C @ intersection ) ) )
| ( C @ ( B @ ( A @ intersection ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[33,388]) ).
thf(448,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ intersection ) @ subset ) ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(45,plain,
( ! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) )
=> ( A = B ) )
& ! [A: $i,B: $i] :
( ( A = B )
=> ( ! [C: $i] :
( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) )
& ! [C: $i] :
( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(46,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E = F )
| ~ ( E @ ( E @ ( F @ sk6 ) @ member ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ member ) ) )
& ( ( E = F )
| ( F @ ( E @ ( F @ sk6 ) @ member ) )
| ~ ( F @ ( E @ ( F @ sk5 ) @ member ) ) )
& ( ( E = F )
| ~ ( E @ ( E @ ( F @ sk6 ) @ member ) )
| ( E @ ( E @ ( F @ sk5 ) @ member ) ) )
& ( ( E = F )
| ( F @ ( E @ ( F @ sk6 ) @ member ) )
| ( E @ ( E @ ( F @ sk5 ) @ member ) ) )
& ( ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ( A != B ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[59]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[53]) ).
thf(1210,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) ) )
| ( B
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) )
| ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[54,11]) ).
thf(1211,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) )
| ( A @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( A @ sk6 ) @ member ) )
| ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( A @ sk5 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[1210:[bind(A,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) )),bind(B,$thf( B ))]]) ).
thf(1338,plain,
( ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk6 ) @ member ) )
| ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk5 ) @ member ) ) ),
inference(simp,[status(thm)],[1211]) ).
thf(65,plain,
( ( ( sk3 @ ( sk2 @ intersection ) )
!= sk3 )
| ( ( sk2 @ ( sk1 @ intersection ) )
!= sk1 ) ),
inference(simp,[status(thm)],[11]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ( B != sk2 )
| ( sk2 != sk1 )
| ( sk3 != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[30,186]) ).
thf(276,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk2 != sk1 )
| ( sk3 != sk1 )
| ~ ( sk3 @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[275:[bind(A,$thf( sk3 ))]]) ).
thf(285,plain,
( ( sk2 != sk1 )
| ( sk3 != sk1 )
| ~ ( sk3 @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(681,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ intersection ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[448,37]) ).
thf(682,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ intersection ) @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) ) ),
inference(simp,[status(thm)],[681]) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[682:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ intersection ) )),bind(D,$thf( G ))]]) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ member ) )
| ~ ( C @ ( B @ intersection ) @ ( A @ member ) ) ),
inference(simp,[status(thm)],[683]) ).
thf(1508,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk6 ) @ member ) )
!= ( A @ ( B @ intersection ) @ ( C @ member ) ) )
| ( B @ ( C @ member ) )
| ~ $true
| ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk5 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[1338,231]) ).
thf(1509,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk6 ) @ member ) )
!= ( A @ ( B @ intersection ) @ ( C @ member ) ) )
| ( B @ ( C @ member ) )
| ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk5 ) @ member ) ) ),
inference(simp,[status(thm)],[1508]) ).
thf(1510,plain,
( ( sk1 @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk6 ) @ member ) )
| ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk5 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[1509:[bind(A,$thf( sk3 @ ( sk2 @ intersection ) )),bind(B,$thf( sk1 )),bind(C,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ sk6 ) ))]]) ).
thf(211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ intersection ) )
!= ( D @ ( C @ intersection ) ) )
| ( C @ ( E @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( E @ member ) ) ),
inference(paramod_ordered,[status(thm)],[33,15]) ).
thf(212,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(219,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( A @ ( B @ intersection ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( sk3 @ ( sk2 @ intersection ) )
!= ( sk2 @ ( sk1 @ intersection ) ) )
| ( A != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[30,155]) ).
thf(198,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ intersection ) )
!= ( sk2 @ ( sk1 @ intersection ) ) )
| ( A != sk1 )
| ~ ( A @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[197:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(208,plain,
( ( ( sk3 @ ( sk2 @ intersection ) )
!= ( sk2 @ ( sk1 @ intersection ) ) )
| ~ ( sk1 @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) ) )
| ( A
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[30,139]) ).
thf(179,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) @ subset ) )
| ~ ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[178:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) ))]]) ).
thf(182,plain,
( ~ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) @ subset ) )
| ~ ( sk2 @ ( sk1 @ intersection ) @ ( sk3 @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ subset ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(26,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[25]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) ) )
| ( B
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[30,11]) ).
thf(105,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) )),bind(B,$thf( B ))]]) ).
thf(126,plain,
( ~ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ subset ) )
| ~ ( sk3 @ ( sk2 @ intersection ) @ ( sk1 @ intersection ) @ ( sk3 @ ( sk2 @ ( sk1 @ intersection ) @ intersection ) @ subset ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ( sk3 != sk2 )
| ( sk2 != sk1 )
| ( B != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[30,186]) ).
thf(272,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( sk2 != sk1 )
| ( A != sk1 )
| ~ ( sk3 @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( sk3 ))]]) ).
thf(283,plain,
( ( sk3 != sk2 )
| ( sk2 != sk1 )
| ~ ( sk3 @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[46]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[61]) ).
thf(7091,plain,
$false,
inference(e,[status(thm)],[253,33,44,155,18,231,254,472,698,42,37,284,448,60,1338,65,285,9,388,701,41,1510,34,12,54,219,208,182,16,31,11,446,40,26,186,139,30,19,126,283,15,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET143+3 : TPTP v9.3.1. Released v2.2.0.
% 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
% 0.14/5.40 % Computer : n005.cluster.edu
% 0.14/5.40 % Model : x86_64 x86_64
% 0.14/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.40 % Memory : 8046.5625MB
% 0.14/5.40 % OS : Linux 6.8.0-71-generic
% 0.14/5.40 % CPULimit : 300
% 0.14/5.40 % WCLimit : 300
% 0.14/5.41 % DateTime : Sat Sep 26 07:12:37 UTC 2026
% 0.14/5.41 % CPUTime :
% 0.14/5.41 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
% 0.18/6.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/6.19 % [INFO] Parsing done (191ms).
% 1.42/6.21 % [INFO] Running in sequential loop mode.
% 2.06/6.62 % [INFO] eprover registered as external prover.
% 2.06/6.63 % [INFO] Scanning for conjecture ...
% 2.27/6.73 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 2.27/6.76 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 2.27/6.78 % [INFO] Problem is first-order (TPTP FOF).
% 2.27/6.78 % [INFO] Type checking passed.
% 2.27/6.79 % [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 ...
% 26.37/11.90 % External prover 'e' found a proof!
% 26.37/11.90 % [INFO] Killing All external provers ...
% 26.37/11.90 % Time passed: 6349ms (effective reasoning time: 5687ms)
% 26.37/11.90 % 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)>
% 26.37/11.90 % Axioms used in derivation (6): reflexivity_of_subset, equal_member_defn, commutativity_of_intersection, equal_defn, subset_defn, intersection_defn
% 26.37/11.90 % No. of inferences in proof: 113
% 26.37/11.91 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6349 ms resp. 5687 ms w/o parsing
% 26.37/12.01 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 26.37/12.01 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------