%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET175+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 : n010.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 08:29:41 AM UTC 2026
% Result : Theorem 27.58s 13.26s
% Output : Refutation 24.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 14
% Syntax : Number of formulae : 104 ( 31 unt; 0 typ; 5 def)
% Number of atoms : 347 ( 83 equ; 0 cnn)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1395 ( 145 ~; 123 |; 37 &;1048 @)
% ( 6 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 235 ( 6 ^; 224 !; 0 ?; 235 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: $i > $i > $i ).
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 > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ intersection ) @ ( A @ union ) )
= A ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ( A @ ( sk1 @ intersection ) @ ( sk1 @ union ) )
!= sk1 ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( B @ ( C @ member ) )
=> ( A @ ( C @ member ) ) ) ) ) ).
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] :
~ ( ( A @ ( C @ member ) )
=> ( B @ ( C @ member ) ) ) ) ) ).
thf(4,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(22,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)],[4]) ).
thf(23,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)],[22]) ).
thf(24,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)],[23]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
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(14,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(5,axiom,
! [A: $i,B: $i] :
( ( A = B )
<=> ( ( A @ ( B @ subset ) )
& ( B @ ( A @ subset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
thf(29,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)],[5]) ).
thf(30,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)],[29]) ).
thf(31,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)],[30]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) )
| ( A = B ) ),
inference(simp,[status(thm)],[39]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) @ ( A @ union ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_absorbtion_for_union) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) @ ( A @ union ) )
= A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(11,plain,
~ ! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) @ ( A @ union ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )
!= sk1 ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )
!= sk1 ),
inference(lifteq,[status(thm)],[12]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( sk2 @ ( sk1 @ intersection ) @ ( A @ union ) )
!= sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[40,13]) ).
thf(97,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( A @ union ) )
!= sk1 )
| ~ ( A @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(8,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(47,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)],[8]) ).
thf(48,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)],[47]) ).
thf(49,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E @ ( D @ subset ) )
| ~ ( E @ ( D @ ( E @ sk3 ) @ member ) ) )
& ( ( E @ ( D @ subset ) )
| ( D @ ( D @ ( E @ sk3 ) @ member ) ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[51]) ).
thf(15,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)],[14]) ).
thf(16,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)],[15]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ( A @ ( C @ member ) )
| ~ ( B @ ( A @ union ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( sk2 @ ( A @ intersection ) @ ( sk1 @ union ) )
!= sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[40,13]) ).
thf(99,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ intersection ) @ ( sk1 @ union ) )
!= sk1 )
| ~ ( A @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(36,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(simp,[status(thm)],[35]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[52]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) ) )
| ( B != sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[40,13]) ).
thf(85,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( A @ subset ) )
| ~ ( A @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )),bind(B,$thf( B ))]]) ).
thf(106,plain,
( ~ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ subset ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ subset ) ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[53,106]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ subset ) ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(342,plain,
( ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[341:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) ))]]) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(20,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[18]) ).
thf(749,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ subset ) ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[54,106]) ).
thf(750,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ subset ) ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[749]) ).
thf(751,plain,
( ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[750:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) ))]]) ).
thf(1343,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) @ ( C @ member ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ $true
| ~ ( A @ ( C @ member ) ) ),
inference(paramod_ordered,[status(thm)],[20,751]) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) @ ( C @ member ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[1343]) ).
thf(1345,plain,
( ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) ),
inference(pattern_uni,[status(thm)],[1344:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) )),bind(C,$thf( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) ))]]) ).
thf(1672,plain,
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) )
!= ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) )
| ~ $true
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[342,1345]) ).
thf(1673,plain,
( ( ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) )
!= ( sk1 @ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ sk3 ) @ member ) ) )
| ~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) ),
inference(simp,[status(thm)],[1672]) ).
thf(1674,plain,
~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ),
inference(pattern_uni,[status(thm)],[1673:[]]) ).
thf(1787,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) )
| ~ $true
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[54,1674]) ).
thf(1788,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) )
| ~ ( B @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[1787]) ).
thf(1789,plain,
~ ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) ),
inference(pattern_uni,[status(thm)],[1788:[bind(A,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )),bind(B,$thf( sk1 ))]]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ intersection ) )
= ( A @ ( B @ intersection ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(10,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(57,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)],[10]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ intersection ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) ) ),
inference(simp,[status(thm)],[27]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ union ) @ ( C @ member ) )
| ~ ( B @ ( C @ member ) ) ),
inference(simp,[status(thm)],[19]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ union ) )
= ( A @ ( B @ union ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) )
| ~ $true
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(paramod_ordered,[status(thm)],[53,1674]) ).
thf(1785,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ subset ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ subset ) ) )
| ( A @ ( A @ ( B @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[1784]) ).
thf(1786,plain,
sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ),
inference(pattern_uni,[status(thm)],[1785:[bind(A,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )),bind(B,$thf( sk1 ))]]) ).
thf(1928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ( B @ ( A @ union ) @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1786,21]) ).
thf(1929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) )
!= ( B @ ( C @ member ) ) )
| ( B @ ( A @ union ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[1928]) ).
thf(1930,plain,
! [A: $i] : ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( A @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) ),
inference(pattern_uni,[status(thm)],[1929:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )),bind(C,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) ))]]) ).
thf(2024,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( A @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1930,1789]) ).
thf(2025,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( A @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) )
!= ( sk1 @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2098,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( A @ union ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) ) ) ),
inference(simp,[status(thm)],[2025]) ).
thf(2129,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( A @ union ) )
!= sk1 ),
inference(simp,[status(thm)],[2098]) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ union ) )
!= ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( C @ union ) ) )
| ( ( A @ ( B @ union ) )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,2129]) ).
thf(2140,plain,
! [A: $i] :
( ( A @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ union ) )
!= sk1 ),
inference(pattern_uni,[status(thm)],[2139:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )),bind(C,$thf( A ))]]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ ( sk1 @ intersection ) @ ( sk1 @ union ) )
!= sk1 )
| ~ ( A @ ( B @ subset ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(paramod_ordered,[status(thm)],[40,13]) ).
thf(103,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ intersection ) @ ( sk1 @ union ) )
!= sk1 )
| ~ ( A @ ( sk2 @ subset ) )
| ~ ( sk2 @ ( A @ subset ) ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ~ ( B @ ( A @ subset ) ) ),
inference(cnfConj,[status(thm)],[49]) ).
thf(58,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)],[57]) ).
thf(59,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( E = F )
| ~ ( E @ ( E @ ( F @ sk5 ) @ member ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ member ) ) )
& ( ( E = F )
| ( F @ ( E @ ( F @ sk5 ) @ member ) )
| ~ ( F @ ( E @ ( F @ sk4 ) @ member ) ) )
& ( ( E = F )
| ~ ( E @ ( E @ ( F @ sk5 ) @ member ) )
| ( E @ ( E @ ( F @ sk4 ) @ member ) ) )
& ( ( E = F )
| ( F @ ( E @ ( F @ sk5 ) @ member ) )
| ( E @ ( E @ ( F @ sk4 ) @ member ) ) )
& ( ( A @ ( D @ member ) )
| ~ ( B @ ( D @ member ) )
| ( A != B ) )
& ( ( B @ ( C @ member ) )
| ~ ( A @ ( C @ member ) )
| ( A != B ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ sk5 ) @ member ) )
| ~ ( B @ ( A @ ( B @ sk4 ) @ member ) )
| ( A = B ) ),
inference(simp,[status(thm)],[66]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ member ) )
| ~ ( B @ ( A @ intersection ) @ ( C @ member ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(1915,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) )
!= ( A @ ( C @ member ) ) )
| ( B @ ( A @ union ) @ ( C @ member ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1786,20]) ).
thf(1916,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) )
!= ( A @ ( C @ member ) ) )
| ( B @ ( A @ union ) @ ( C @ member ) ) ),
inference(simp,[status(thm)],[1915]) ).
thf(1917,plain,
! [A: $i] : ( A @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) ),
inference(pattern_uni,[status(thm)],[1916:[bind(A,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) )),bind(B,$thf( B )),bind(C,$thf( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) ))]]) ).
thf(2004,plain,
! [A: $i] : ( A @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ union ) @ ( sk2 @ ( sk1 @ intersection ) @ ( sk1 @ union ) @ ( sk1 @ sk3 ) @ member ) ),
inference(simp,[status(thm)],[1917]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
thf(55,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3832,plain,
$false,
inference(e,[status(thm)],[25,14,97,53,17,99,36,1789,20,46,57,29,28,21,13,41,2140,22,44,1786,54,2129,103,50,67,11,43,1674,40,26,2004,55,1930,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET175+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
% 0.18/6.06 % Computer : n010.cluster.edu
% 0.18/6.06 % Model : x86_64 x86_64
% 0.18/6.06 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/6.06 % Memory : 8046.5625MB
% 0.18/6.06 % OS : Linux 6.8.0-71-generic
% 0.18/6.06 % CPULimit : 300
% 0.18/6.06 % WCLimit : 300
% 0.18/6.06 % DateTime : Sat Sep 26 07:17:09 UTC 2026
% 0.18/6.07 % CPUTime :
% 0.18/6.07 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
% 1.42/6.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/7.23 % [INFO] Parsing done (286ms).
% 1.95/7.25 % [INFO] Running in sequential loop mode.
% 2.92/7.88 % [INFO] eprover registered as external prover.
% 2.92/7.89 % [INFO] Scanning for conjecture ...
% 3.14/8.05 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.42/8.09 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.42/8.11 % [INFO] Problem is first-order (TPTP FOF).
% 3.42/8.12 % [INFO] Type checking passed.
% 3.42/8.12 % [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 ...
% 27.58/13.25 % External prover 'e' found a proof!
% 27.58/13.25 % [INFO] Killing All external provers ...
% 27.58/13.25 % Time passed: 6971ms (effective reasoning time: 5993ms)
% 27.58/13.25 % 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)>
% 27.58/13.26 % Axioms used in derivation (8): reflexivity_of_subset, equal_member_defn, equal_defn, intersection_defn, commutativity_of_intersection, commutativity_of_union, union_defn, subset_defn
% 27.58/13.26 % No. of inferences in proof: 99
% 27.58/13.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6971 ms resp. 5993 ms w/o parsing
% 24.01/13.40 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.01/13.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------