%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n011.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 08:31:19 AM UTC 2026
% Result : Theorem 9.37s 4.02s
% Output : Refutation 10.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 134 ( 68 unt; 0 typ; 8 def)
% Number of atoms : 374 ( 157 equ; 0 cnn)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 1193 ( 186 ~; 96 |; 46 &; 837 @)
% ( 4 <=>; 24 =>; 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 : 17 ( 14 usr; 7 con; 0-3 aty)
% Number of variables : 310 ( 8 ^; 276 !; 18 ?; 310 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(disjoint_decl,type,
disjoint: $i > $i > $o ).
thf(unordered_pair_decl,type,
unordered_pair: $i > $i > $i ).
thf(set_intersection2_decl,type,
set_intersection2: $i > $i > $i ).
thf(empty_decl,type,
empty: $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 > $o ).
thf(sk5_decl,type,
sk5: $i > $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i ).
thf(sk11_decl,type,
sk11: $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
? [B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ ( A @ unordered_pair ) @ disjoint ) )
& ~ ( B @ ( C @ in ) ) )
& ~ ( B @ ( A @ in ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
( ? [B: $i] :
( ~ ( A @ ( B @ ( sk1 @ unordered_pair ) @ disjoint ) )
& ~ ( A @ ( B @ in ) ) )
& ~ ( A @ ( sk1 @ in ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
( ~ ( sk2 @ ( A @ ( sk1 @ unordered_pair ) @ disjoint ) )
& ~ ( sk2 @ ( A @ in ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( A @ ( D @ in ) )
=> ( ( D = B )
| ( D = C ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i,C: $i] :
@+[D: $i] :
~ ( ( ( D = B )
| ( D = C ) )
=> ( A @ ( D @ in ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( @+[A: $i] : ( A @ empty ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( @+[A: $i] :
~ ( A @ empty ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] : ( A @ ( B @ set_intersection2 ) @ ( C @ in ) ) ) ) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
thf(21,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(22,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
= ( A @ ( B @ unordered_pair ) ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
<=> ! [D: $i] :
( ( C @ ( D @ in ) )
<=> ( ( D = B )
| ( D = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_tarski) ).
thf(27,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)],[6]) ).
thf(28,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)],[27]) ).
thf(29,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 @ sk6 ) ) @ in ) )
| ( H @ ( G @ ( F @ sk4 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
= G )
| ( ( F @ ( G @ ( H @ sk6 ) ) )
= F )
| ( H @ ( G @ ( F @ sk4 ) ) ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk4 ) ) )
| ( ( F @ ( G @ ( H @ sk5 ) ) )
!= G ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk4 ) ) )
| ( ( F @ ( G @ ( H @ sk5 ) ) )
!= F ) )
& ( ( H
= ( G @ ( F @ unordered_pair ) ) )
| ~ ( H @ ( G @ ( F @ sk4 ) ) )
| ( H @ ( F @ ( G @ ( H @ sk5 ) ) @ 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)],[28]) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(38,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != A )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( A @ in ) ),
inference(simp,[status(thm)],[38]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(19,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ in ) )
| ~ ( B @ ( A @ in ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( B @ ( A @ in ) ) ),
inference(eqfactor_ordered,[status(thm)],[20]) ).
thf(115,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( B ))]]) ).
thf(117,plain,
! [A: $i] :
~ ( A @ ( A @ in ) ),
inference(simp,[status(thm)],[115]) ).
thf(119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,117]) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( C @ in ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( A != C ) ),
inference(simp,[status(thm)],[120]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[121]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( C @ ( D @ unordered_pair ) ) )
| ( ( A @ ( B @ unordered_pair ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[23,122]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ unordered_pair ) )
!= A ),
inference(pattern_uni,[status(thm)],[169:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ in ) )
| ( D != B )
| ( C
!= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(47,plain,
! [B: $i,A: $i] : ( B @ ( A @ unordered_pair ) @ ( B @ in ) ),
inference(simp,[status(thm)],[46]) ).
thf(133,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,117]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( C @ in ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( B != C ) ),
inference(simp,[status(thm)],[134]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[137]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ unordered_pair ) @ disjoint ) )
& ~ ( B @ ( C @ in ) )
& ~ ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ unordered_pair ) @ disjoint ) )
& ~ ( B @ ( C @ in ) )
& ~ ( B @ ( A @ in ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i,C: $i] :
~ ( ~ ( B @ ( C @ ( A @ unordered_pair ) @ disjoint ) )
& ~ ( B @ ( C @ in ) )
& ~ ( B @ ( A @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(14,plain,
~ ~ ? [A: $i,B: $i] :
( ? [C: $i] :
( ~ ( B @ ( C @ ( A @ unordered_pair ) @ disjoint ) )
& ~ ( B @ ( C @ in ) ) )
& ~ ( B @ ( A @ in ) ) ),
inference(miniscope,[status(thm)],[13]) ).
thf(15,plain,
( ~ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ disjoint ) )
& ~ ( sk2 @ ( sk3 @ in ) )
& ~ ( sk2 @ ( sk1 @ in ) ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
~ ( sk2 @ ( sk1 @ in ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ~ ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk4 ) ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( C @ sk6 ) ) @ in ) )
| ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[42]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',t4_xboole_0) ).
thf(91,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)],[12]) ).
thf(92,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)],[91]) ).
thf(93,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 @ sk12 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ) ),
inference(cnf,[status(esa)],[92]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk12 ) @ in ) )
| ( B @ ( A @ disjoint ) ) ),
inference(cnfConj,[status(thm)],[93]) ).
thf(18,plain,
~ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ disjoint ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ disjoint ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ disjoint ) ) )
| ~ $true
| ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk12 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[94,18]) ).
thf(289,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ disjoint ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ disjoint ) ) )
| ( B @ ( A @ set_intersection2 ) @ ( A @ ( B @ sk12 ) @ in ) ) ),
inference(simp,[status(thm)],[288]) ).
thf(290,plain,
sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( sk3 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( sk2 ))]]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( D @ in ) ) )
| ~ $true
| ~ ( D @ ( C @ in ) ) ),
inference(paramod_ordered,[status(thm)],[47,20]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( D @ in ) ) )
| ~ ( D @ ( C @ in ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ unordered_pair ) )),bind(D,$thf( F ))]]) ).
thf(138,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[128]) ).
thf(10,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(86,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(87,plain,
~ ! [A: $i] : ( A @ empty ),
inference(miniscope,[status(thm)],[86]) ).
thf(88,plain,
~ ( sk11 @ empty ),
inference(cnf,[status(esa)],[87]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,20]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) )
!= ( B @ ( A @ in ) ) )
| ~ ( A @ ( B @ in ) ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
~ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ in ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) )),bind(B,$thf( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ))]]) ).
thf(17,plain,
~ ( sk2 @ ( sk3 @ in ) ),
inference(cnfConj,[status(thm)],[15]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,17]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[101]) ).
thf(106,plain,
! [A: $i] :
( ( A @ ( sk3 @ unordered_pair ) )
!= sk2 ),
inference(simp,[status(thm)],[104]) ).
thf(9,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(84,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ disjoint ) )
=> ( A @ ( B @ disjoint ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(111,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( D @ in ) ) )
| ~ $true
| ~ ( D @ ( C @ in ) ) ),
inference(paramod_ordered,[status(thm)],[39,20]) ).
thf(112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( D @ in ) ) )
| ~ ( D @ ( C @ in ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ unordered_pair ) )),bind(D,$thf( E ))]]) ).
thf(116,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ ( A @ unordered_pair ) @ in ) ),
inference(simp,[status(thm)],[113]) ).
thf(85,plain,
sk10 @ empty,
inference(cnf,[status(esa)],[84]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= A )
| ( C @ ( B @ ( A @ sk4 ) ) ) ),
inference(cnfConj,[status(thm)],[29]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= A ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ sk4 ) ) )
| ( C
= ( B @ ( A @ unordered_pair ) ) )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= B )
| ( ( A @ ( B @ ( C @ sk6 ) ) )
= A ) ),
inference(simp,[status(thm)],[40]) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ( ( B @ ( A @ unordered_pair ) )
!= D ) ),
inference(paramod_ordered,[status(thm)],[23,141]) ).
thf(180,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) )
!= A ),
inference(pattern_uni,[status(thm)],[179:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(7,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/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
thf(54,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)],[7]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
thf(81,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(335,plain,
! [A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[290,117]) ).
thf(336,plain,
! [A: $i] :
( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) )
!= ( A @ ( A @ in ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(355,plain,
! [A: $i] :
( ( ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) )
!= A )
| ( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) )
!= A ) ),
inference(simp,[status(thm)],[336]) ).
thf(362,plain,
( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( D @ ( C @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,116]) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( C @ ( D @ ( C @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( A
!= ( D @ ( C @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(208,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ unordered_pair ) @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[206]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,17]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ ( sk3 @ in ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( B != sk3 ) ),
inference(simp,[status(thm)],[130]) ).
thf(140,plain,
! [A: $i] :
( ( sk3 @ ( A @ unordered_pair ) )
!= sk2 ),
inference(simp,[status(thm)],[136]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( D @ ( C @ unordered_pair ) @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,116]) ).
thf(201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( C @ ( D @ ( C @ unordered_pair ) @ in ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= C )
| ( B
!= ( D @ ( C @ unordered_pair ) ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ unordered_pair ) @ ( A @ unordered_pair ) )
!= B ),
inference(simp,[status(thm)],[207]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ set_intersection2 ) )
= ( A @ ( B @ set_intersection2 ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(341,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ set_intersection2 ) )
!= ( sk2 @ ( sk3 @ ( sk1 @ unordered_pair ) @ set_intersection2 ) ) )
| ( A @ ( B @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[26,290]) ).
thf(342,plain,
sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ),
inference(pattern_uni,[status(thm)],[341:[bind(A,$thf( sk3 @ ( sk1 @ unordered_pair ) )),bind(B,$thf( sk2 ))]]) ).
thf(662,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) )
!= ( A @ ( A @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[342,117]) ).
thf(663,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) @ ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) @ in ) )
!= ( A @ ( A @ in ) ) ),
inference(simp,[status(thm)],[662]) ).
thf(682,plain,
! [A: $i] :
( ( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) )
!= A )
| ( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) )
!= A ) ),
inference(simp,[status(thm)],[663]) ).
thf(690,plain,
( ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ sk12 ) )
!= ( sk3 @ ( sk1 @ unordered_pair ) @ ( sk2 @ set_intersection2 ) ) ),
inference(simp,[status(thm)],[682]) ).
thf(97,plain,
( ( ( sk11 @ empty )
!= ( sk10 @ empty ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[85,88]) ).
thf(98,plain,
( ( sk11 @ empty )
!= ( sk10 @ empty ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
sk11 != sk10,
inference(simp,[status(thm)],[98]) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ~ ( C @ ( A @ ( B @ unordered_pair ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[23,116]) ).
thf(203,plain,
! [B: $i,A: $i] :
~ ( A @ ( A @ ( B @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[202:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,16]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( B @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( B != sk1 ) ),
inference(simp,[status(thm)],[132]) ).
thf(139,plain,
! [A: $i] :
( ( sk1 @ ( A @ unordered_pair ) )
!= sk2 ),
inference(simp,[status(thm)],[135]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39,16]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ unordered_pair ) @ ( A @ in ) )
!= ( sk2 @ ( sk1 @ in ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= sk2 )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[103]) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( sk1 @ unordered_pair ) )
!= sk2 ),
inference(simp,[status(thm)],[105]) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
! [A: $i] :
( ( A @ ( A @ set_intersection2 ) )
= A ),
inference(lifteq,[status(thm)],[82]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ unordered_pair ) )
!= ( D @ ( C @ unordered_pair ) ) )
| ~ ( D @ ( A @ ( B @ unordered_pair ) @ in ) ) ),
inference(paramod_ordered,[status(thm)],[23,138]) ).
thf(215,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ ( B @ unordered_pair ) @ in ) ),
inference(pattern_uni,[status(thm)],[214:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B ))]]) ).
thf(814,plain,
$false,
inference(e,[status(thm)],[170,24,21,141,27,16,43,290,19,47,138,88,20,325,106,84,89,116,117,85,13,41,180,17,54,86,81,362,39,208,140,91,209,342,690,18,99,203,26,139,23,107,94,122,83,215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET916+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.55 % Computer : n011.cluster.edu
% 0.12/0.55 % Model : x86_64 x86_64
% 0.12/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.55 % Memory : 8046.5625MB
% 0.12/0.55 % OS : Linux 6.8.0-71-generic
% 0.12/0.55 % CPULimit : 300
% 0.12/0.55 % WCLimit : 300
% 0.12/0.55 % DateTime : Sat Sep 26 08:25:29 UTC 2026
% 0.12/0.55 % CPUTime :
% 0.12/0.55 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.98/1.14 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.29/1.34 % [INFO] Parsing done (197ms).
% 1.29/1.35 % [INFO] Running in sequential loop mode.
% 1.97/1.75 % [INFO] eprover registered as external prover.
% 1.97/1.76 % [INFO] Scanning for conjecture ...
% 2.19/1.86 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 2.34/1.90 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.34/1.93 % [INFO] Problem is first-order (TPTP FOF).
% 2.34/1.93 % [INFO] Type checking passed.
% 2.34/1.94 % [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 ...
% 9.37/4.01 % External prover 'e' found a proof!
% 9.37/4.01 % [INFO] Killing All external provers ...
% 9.37/4.02 % Time passed: 3326ms (effective reasoning time: 2660ms)
% 9.37/4.02 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.37/4.02 % Axioms used in derivation (10): idempotence_k3_xboole_0, commutativity_k3_xboole_0, d2_tarski, t4_xboole_0, commutativity_k2_tarski, rc1_xboole_0, symmetry_r1_xboole_0, rc2_xboole_0, d3_xboole_0, antisymmetry_r2_hidden
% 9.37/4.02 % No. of inferences in proof: 126
% 9.37/4.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3326 ms resp. 2660 ms w/o parsing
% 10.21/4.12 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.21/4.12 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------