%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET159+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 : n002.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 08:29:38 AM UTC 2026
% Result : Theorem 41.57s 10.51s
% Output : Refutation 34.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 13
% Syntax : Number of formulae : 121 ( 22 unt; 0 typ; 6 def)
% Number of atoms : 405 ( 123 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1423 ( 185 ~; 193 |; 28 &; 980 @)
% ( 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 : 315 ( 6 ^; 303 !; 0 ?; 315 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: $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 @ union ) @ union ) )
= ( C @ ( B @ union ) @ ( A @ union ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ ( sk1 @ union ) @ union ) )
= ( B @ ( A @ union ) @ ( sk1 @ union ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ( A @ ( sk2 @ ( sk1 @ union ) @ union ) )
!= ( A @ ( sk2 @ union ) @ ( sk1 @ union ) ) ) ) ) ).
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(4,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(20,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(21,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)],[20]) ).
thf(22,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)],[21]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[30]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ union ) @ union ) )
= ( C @ ( B @ union ) @ ( A @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_associativity_of_union) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ union ) @ union ) )
= ( C @ ( B @ union ) @ ( A @ union ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(9,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ union ) @ union ) )
= ( C @ ( B @ union ) @ ( A @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) )
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(11,plain,
( ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) )
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) ) )
| ( ( A @ ( B @ union ) )
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) ) ),
inference(paramod_ordered,[status(thm)],[34,11]) ).
thf(148,plain,
( ( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) )
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( sk2 @ ( sk1 @ union ) )),bind(B,$thf( sk3 ))]]) ).
thf(156,plain,
( ( ( sk3 @ ( sk2 @ union ) )
!= ( sk2 @ ( sk1 @ union ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[148]) ).
thf(187,plain,
( ( sk3 != sk2 )
| ( sk2 != sk1 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[156]) ).
thf(296,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( sk3 != sk2 )
| ( B != sk1 )
| ( sk3 != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,187]) ).
thf(297,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( A != sk1 )
| ( sk3 != sk1 )
| ~ ( sk2 @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[296:[bind(A,$thf( sk2 ))]]) ).
thf(308,plain,
( ( sk3 != sk2 )
| ( sk3 != sk1 )
| ~ ( sk2 @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[297]) ).
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(35,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(36,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)],[35]) ).
thf(37,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)],[36]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
<=> ( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
thf(12,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) ) )
=> ( B @ ( A @ union ) @ ( C @ member ) ) )
& ( ( B @ ( A @ union ) @ ( 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 @ union ) @ ( C @ member ) ) )
& ! [A: $i,B: $i,C: $i] :
( ( B @ ( A @ union ) @ ( 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 @ union ) @ ( F @ member ) )
| ~ ( E @ ( F @ member ) ) )
& ( ( E @ ( D @ union ) @ ( F @ member ) )
| ~ ( D @ ( F @ member ) ) )
& ( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) )
| ~ ( B @ ( A @ union ) @ ( C @ member ) ) ) ),
inference(cnf,[status(esa)],[13]) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( C @ ( E @ member ) ) )
| ( D @ ( C @ union ) @ ( E @ member ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[41,18]) ).
thf(271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( C @ ( E @ member ) ) )
| ( D @ ( C @ union ) @ ( E @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ union ) @ ( C @ ( B @ sk4 ) @ member ) )
| ( B @ ( C @ subset ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ union ) @ ( C @ ( B @ sk4 ) @ member ) )
| ( B @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ union ) @ ( C @ ( B @ sk4 ) @ member ) )
!= ( E @ ( D @ ( E @ sk4 ) @ member ) ) )
| ( E @ ( D @ subset ) )
| ~ $true
| ( B @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[289,42]) ).
thf(447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ union ) @ ( C @ ( B @ sk4 ) @ member ) )
!= ( E @ ( D @ ( E @ sk4 ) @ member ) ) )
| ( E @ ( D @ subset ) )
| ( B @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[446]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( A @ subset ) )
| ( B @ ( A @ union ) @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( G )),bind(B,$thf( G @ ( F @ union ) )),bind(C,$thf( F )),bind(D,$thf( F )),bind(E,$thf( G @ ( F @ union ) ))]]) ).
thf(480,plain,
! [B: $i,A: $i] : ( B @ ( A @ union ) @ ( A @ subset ) ),
inference(simp,[status(thm)],[448]) ).
thf(294,plain,
! [B: $i,A: $i] :
( ( A != sk3 )
| ( sk3 != sk2 )
| ( sk2 != sk1 )
| ( B != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,187]) ).
thf(295,plain,
! [A: $i] :
( ( sk3 != sk2 )
| ( sk2 != sk1 )
| ( A != sk1 )
| ~ ( sk3 @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ subset ) ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( sk3 ))]]) ).
thf(307,plain,
( ( sk3 != sk2 )
| ( sk2 != sk1 )
| ~ ( sk3 @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( sk3 @ subset ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[37]) ).
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(45,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(46,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)],[45]) ).
thf(47,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)],[46]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[64]) ).
thf(391,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( C @ ( E @ union ) ) )
| ( A @ ( B @ union ) @ ( E @ ( D @ sk4 ) @ member ) )
| ( D @ ( E @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[34,289]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ union ) @ ( A @ ( C @ sk4 ) @ member ) )
| ( C @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[391:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( A ))]]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ union ) @ ( A @ ( C @ sk4 ) @ member ) )
| ( C @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[392]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(27,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[26]) ).
thf(66,plain,
( ( ( sk3 @ ( sk2 @ union ) )
!= sk3 )
| ( ( sk2 @ ( sk1 @ union ) )
!= sk1 ) ),
inference(simp,[status(thm)],[11]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[54]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( sk3 @ ( sk2 @ union ) )
!= sk3 )
| ( ( sk2 @ ( A @ union ) )
!= sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,66]) ).
thf(82,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ union ) )
!= sk3 )
| ( ( sk2 @ ( A @ union ) )
!= sk1 )
| ~ ( A @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( D @ ( C @ union ) ) )
| ( A @ ( B @ union ) @ ( C @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[34,480]) ).
thf(506,plain,
! [B: $i,A: $i] : ( A @ ( B @ union ) @ ( A @ subset ) ),
inference(pattern_uni,[status(thm)],[505:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) )
| ~ ( B @ ( A @ union ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[14]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) ) )
| ( B
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,11]) ).
thf(100,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) )
| ~ ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) @ ( A @ subset ) )
| ~ ( A @ ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) )),bind(B,$thf( B ))]]) ).
thf(122,plain,
( ~ ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) @ ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) @ subset ) )
| ~ ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) @ ( sk3 @ ( sk2 @ ( sk1 @ union ) @ union ) @ subset ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[56]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ sk6 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk5 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[60]) ).
thf(283,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ( D @ ( C @ union ) @ ( E @ member ) )
| ~ $true
| ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[41,19]) ).
thf(284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ sk4 ) @ member ) )
!= ( D @ ( E @ member ) ) )
| ( D @ ( C @ union ) @ ( E @ member ) )
| ( B @ ( A @ subset ) ) ),
inference(simp,[status(thm)],[283]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ union ) @ ( C @ ( B @ sk4 ) @ member ) )
| ( B @ ( C @ subset ) ) ),
inference(pattern_uni,[status(thm)],[284:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( G )),bind(E,$thf( G @ ( F @ sk4 ) ))]]) ).
thf(293,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ union ) @ ( C @ ( B @ sk4 ) @ member ) )
| ( B @ ( C @ subset ) ) ),
inference(simp,[status(thm)],[285]) ).
thf(488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) @ ( A @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[480,38]) ).
thf(489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) @ ( A @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) ) ),
inference(simp,[status(thm)],[488]) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[489:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( F )),bind(D,$thf( G @ ( F @ union ) ))]]) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( B @ ( A @ member ) ) ),
inference(simp,[status(thm)],[490]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( ( sk3 @ ( sk2 @ union ) )
!= ( sk2 @ ( sk1 @ union ) ) )
| ( A != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,156]) ).
thf(197,plain,
! [A: $i] :
( ( ( sk3 @ ( sk2 @ union ) )
!= ( sk2 @ ( sk1 @ union ) ) )
| ( A != sk1 )
| ~ ( A @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[196:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(208,plain,
( ( ( sk3 @ ( sk2 @ union ) )
!= ( sk2 @ ( sk1 @ union ) ) )
| ~ ( sk1 @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( sk1 @ subset ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(393,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ union ) )
!= ( C @ ( E @ union ) ) )
| ( B @ ( A @ union ) @ ( E @ ( D @ sk4 ) @ member ) )
| ( D @ ( E @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[34,289]) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( B @ ( C @ sk4 ) @ member ) )
| ( C @ ( B @ subset ) ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( B @ ( C @ sk4 ) @ member ) )
| ( C @ ( B @ subset ) ) ),
inference(simp,[status(thm)],[394]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( B != sk3 )
| ( A != sk2 )
| ( sk2 != sk1 )
| ( sk3 != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,187]) ).
thf(305,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk2 != sk1 )
| ( sk3 != sk1 )
| ~ ( A @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[304:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(306,plain,
( ( sk2 != sk1 )
| ( sk3 != sk1 )
| ~ ( sk2 @ ( sk3 @ subset ) )
| ~ ( sk3 @ ( sk2 @ subset ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(234,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( D @ ( C @ union ) ) )
| ( A @ ( B @ union ) @ ( E @ member ) )
| ~ ( C @ ( E @ member ) ) ),
inference(paramod_ordered,[status(thm)],[34,18]) ).
thf(235,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ union ) @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(241,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ union ) @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( D @ ( C @ union ) ) )
| ( A @ ( B @ union ) @ ( E @ member ) )
| ~ ( D @ ( E @ member ) ) ),
inference(paramod_ordered,[status(thm)],[34,19]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ union ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(263,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ union ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[260]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) ) )
| ( A
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[31,148]) ).
thf(176,plain,
! [A: $i] :
( ( A
!= ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) ) )
| ~ ( A @ ( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) @ subset ) )
| ~ ( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[175:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) ))]]) ).
thf(182,plain,
( ~ ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) @ ( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) @ subset ) )
| ~ ( sk2 @ ( sk1 @ union ) @ ( sk3 @ union ) @ ( sk3 @ ( sk2 @ union ) @ ( sk1 @ union ) @ subset ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ union ) @ ( A @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[506,38]) ).
thf(519,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ union ) @ ( A @ subset ) )
!= ( D @ ( C @ subset ) ) )
| ( D @ ( E @ member ) )
| ~ ( C @ ( E @ member ) ) ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) ) ),
inference(pattern_uni,[status(thm)],[519:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( G @ ( F @ union ) ))]]) ).
thf(544,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ union ) @ ( A @ member ) )
| ~ ( C @ ( A @ member ) ) ),
inference(simp,[status(thm)],[520]) ).
thf(7,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(43,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(10497,plain,
$false,
inference(e,[status(thm)],[308,42,480,307,38,65,398,27,12,66,55,82,19,506,15,122,20,289,57,61,293,156,9,515,41,148,45,32,34,187,208,399,306,241,35,18,263,182,544,31,11,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET159+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.12 % 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
% 0.20/0.48 % Computer : n002.cluster.edu
% 0.20/0.48 % Model : x86_64 x86_64
% 0.20/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.48 % Memory : 8046.5625MB
% 0.20/0.48 % OS : Linux 6.8.0-71-generic
% 0.20/0.49 % CPULimit : 300
% 0.20/0.49 % WCLimit : 300
% 0.20/0.49 % DateTime : Sat Sep 26 07:17:20 UTC 2026
% 0.20/0.49 % CPUTime :
% 0.20/0.49 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
% 1.35/1.34 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.84/1.61 % [INFO] Parsing done (261ms).
% 1.84/1.63 % [INFO] Running in sequential loop mode.
% 2.78/2.24 % [INFO] eprover registered as external prover.
% 2.78/2.25 % [INFO] Scanning for conjecture ...
% 2.96/2.38 % [INFO] Found a conjecture (or negated_conjecture) and 6 axioms. Running axiom selection ...
% 3.14/2.43 % [INFO] Axiom selection finished. Selected 6 axioms (removed 0 axioms).
% 3.14/2.46 % [INFO] Problem is first-order (TPTP FOF).
% 3.14/2.47 % [INFO] Type checking passed.
% 3.14/2.47 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 41.57/10.50 % External prover 'e' found a proof!
% 41.57/10.50 % [INFO] Killing All external provers ...
% 41.57/10.50 % Time passed: 9796ms (effective reasoning time: 8863ms)
% 41.57/10.50 % 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)>
% 41.57/10.51 % Axioms used in derivation (6): reflexivity_of_subset, equal_member_defn, commutativity_of_union, equal_defn, union_defn, subset_defn
% 41.57/10.51 % No. of inferences in proof: 115
% 41.57/10.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9796 ms resp. 8863 ms w/o parsing
% 34.91/10.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.91/10.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------