%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU610^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : Wed Sep 30 08:28:45 AM UTC 2026
% Result : Theorem 4.98s 2.80s
% Output : Refutation 5.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 15 unt; 0 typ; 7 def)
% Number of atoms : 153 ( 37 equ; 0 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 406 ( 40 ~; 36 |; 6 &; 280 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 99 ( 2 ^; 93 !; 1 ?; 99 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(in__Cong_decl,type,
in__Cong: $o ).
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(subsetI2_decl,type,
subsetI2: $o ).
thf(setminus_decl,type,
setminus: $i > $i > $i ).
thf(setminusI_decl,type,
setminusI: $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(in__Cong_def,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) ) ) ) ).
thf(subsetI2_def,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) ) ) ) ).
thf(setminusI_def,definition,
( setminusI
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( in @ C @ B )
=> ( in @ C @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( ( setminus @ sk2 @ A )
= emptyset )
=> ( subset @ sk2 @ A ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( in__Cong
=> ( subsetI2
=> ( setminusI
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [C: $i,D: $i] :
( ( C = D )
=> ( ( in @ C @ A )
= ( in @ D @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ A )
=> ( in @ C @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ A )
=> ( ~ ( in @ C @ B )
=> ( in @ C @ ( setminus @ A @ B ) ) ) )
=> ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( ( C != D )
| ( E != F )
| ( ( in @ E @ C )
= ( in @ F @ D ) ) )
& ( ( in @ ( sk1 @ H @ G ) @ G )
| ( subset @ G @ H ) )
& ( ~ ( in @ ( sk1 @ H @ G ) @ H )
| ( subset @ G @ H ) )
& ( ~ ( in @ K @ I )
| ( in @ K @ J )
| ( in @ K @ ( setminus @ I @ J ) ) )
& ( ( setminus @ sk2 @ sk3 )
= emptyset )
& ~ ( subset @ sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[4]) ).
thf(8,plain,
( ( setminus @ sk2 @ sk3 )
= emptyset ),
inference(cnfConj,[status(thm)],[5]) ).
thf(18,plain,
( ( setminus @ sk2 @ sk3 )
= emptyset ),
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[10]) ).
thf(11,plain,
~ ( subset @ sk2 @ sk3 ),
inference(cnfConj,[status(thm)],[5]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ~ $true
| ( ( subset @ A @ B )
!= ( subset @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[13,11]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ A )
| ( ( subset @ A @ B )
!= ( subset @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
in @ ( sk1 @ sk3 @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(12,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( in @ C @ A )
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) ) ),
inference(simp,[status(thm)],[12]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) )
| ( ( in @ ( sk1 @ sk3 @ sk2 ) @ sk2 )
!= ( in @ C @ A ) ) ),
inference(paramod_ordered,[status(thm)],[49,17]) ).
thf(104,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ C @ B )
| ( in @ C @ ( setminus @ A @ B ) )
| ( ( in @ ( sk1 @ sk3 @ sk2 ) @ sk2 )
!= ( in @ C @ A ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(105,plain,
! [A: $i] :
( ( in @ ( sk1 @ sk3 @ sk2 ) @ A )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ ( setminus @ sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk2 )),bind(B,$thf( B )),bind(C,$thf( sk1 @ sk3 @ sk2 ))]]) ).
thf(114,plain,
! [A: $i] :
( ( in @ ( sk1 @ sk3 @ sk2 ) @ A )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ ( setminus @ sk2 @ A ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(132,plain,
! [A: $i] :
( ( in @ ( sk1 @ sk3 @ sk2 ) @ A )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ emptyset )
| ( ( setminus @ sk2 @ sk3 )
!= ( setminus @ sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[18,114]) ).
thf(133,plain,
( ( in @ ( sk1 @ sk3 @ sk2 ) @ sk3 )
| ( in @ ( sk1 @ sk3 @ sk2 ) @ emptyset ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( sk3 ))]]) ).
thf(7,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(22,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ~ $true
| ( B
!= ( subset @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[7,11]) ).
thf(23,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( subset @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[23:[bind(A,$thf( A )),bind(B,$thf( subset @ sk2 @ sk3 ))]]) ).
thf(6,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( subset @ A @ B ) ),
inference(simp,[status(thm)],[6]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ~ $true
| ( ( subset @ A @ B )
!= ( subset @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[14,11]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( in @ ( sk1 @ B @ A ) @ B )
| ( ( subset @ A @ B )
!= ( subset @ sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
~ ( in @ ( sk1 @ sk3 @ sk2 ) @ sk3 ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(200,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[133,24,60]) ).
thf(201,plain,
$false,
inference(simp,[status(thm)],[200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU610^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.10/0.21 % Computer : n002.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 14:00:23 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 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
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.99 % [INFO] Parsing done (179ms).
% 1.23/1.01 % [INFO] Running in sequential loop mode.
% 2.03/1.41 % [INFO] eprover registered as external prover.
% 2.03/1.42 % [INFO] Scanning for conjecture ...
% 2.23/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.23/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.23/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.23/1.58 % [INFO] Type checking passed.
% 2.23/1.59 % [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 ...
% 4.98/2.79 % [INFO] Killing All external provers ...
% 4.98/2.79 % Time passed: 2416ms (effective reasoning time: 1776ms)
% 4.98/2.79 % 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)>
% 4.98/2.80 % Axioms used in derivation (0):
% 4.98/2.80 % No. of inferences in proof: 32
% 4.98/2.80 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2416 ms resp. 1776 ms w/o parsing
% 5.27/2.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.27/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------