%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU519^2 : 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 08:28:22 AM UTC 2026
% Result : Theorem 5.32s 3.04s
% Output : Refutation 5.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 62 ( 8 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 20 ~; 12 |; 3 &; 120 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 2 ^; 41 !; 1 ?; 46 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(powersetI_decl,type,
powersetI: $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(powersetI_def,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
~ ( ( in @ C @ A )
=> ( in @ C @ B ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ( powersetI
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [D: $i,C: $i,B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( ( in @ ( sk1 @ D @ C ) @ D )
| ( in @ D @ ( powerset @ C ) ) )
& ( ~ ( in @ ( sk1 @ D @ C ) @ C )
| ( in @ D @ ( powerset @ C ) ) )
& ~ ( in @ emptyset @ ( powerset @ sk2 ) ) ),
inference(cnf,[status(esa)],[4]) ).
thf(9,plain,
~ ( in @ emptyset @ ( powerset @ sk2 ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(7,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(cnfConj,[status(thm)],[5]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ( in @ ( sk1 @ B @ A ) @ B )
| ( in @ B @ ( powerset @ A ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(6,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(15,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ~ $true
| ( B
!= ( in @ emptyset @ ( powerset @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[6,9]) ).
thf(16,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| ( B
!= ( in @ emptyset @ ( powerset @ sk2 ) ) ) ),
inference(simp,[status(thm)],[15]) ).
thf(17,plain,
! [A: $i] :
~ ( in @ A @ emptyset ),
inference(pattern_uni,[status(thm)],[16:[bind(A,$thf( A )),bind(B,$thf( in @ emptyset @ ( powerset @ sk2 ) ))]]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ~ $true
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[10,17]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( in @ B @ ( powerset @ A ) )
| ( ( in @ ( sk1 @ B @ A ) @ B )
!= ( in @ C @ emptyset ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(38,plain,
! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( E )),bind(B,$thf( emptyset )),bind(C,$thf( sk1 @ emptyset @ E ))]]) ).
thf(45,plain,
! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ),
inference(simp,[status(thm)],[38]) ).
thf(48,plain,
~ $true,
inference(rewrite,[status(thm)],[9,45]) ).
thf(49,plain,
$false,
inference(simp,[status(thm)],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU519^2 : 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
% 0.11/0.21 % Computer : n002.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 13:50:22 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.20/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.74/1.28 % [INFO] Parsing done (272ms).
% 1.74/1.30 % [INFO] Running in sequential loop mode.
% 2.85/1.91 % [INFO] eprover registered as external prover.
% 2.85/1.92 % [INFO] Scanning for conjecture ...
% 3.14/2.07 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 3.14/2.12 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 3.14/2.13 % [INFO] Problem is higher-order (TPTP THF).
% 3.14/2.13 % [INFO] Type checking passed.
% 3.14/2.14 % [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 ...
% 5.32/3.03 % [INFO] Killing All external provers ...
% 5.32/3.03 % Time passed: 2623ms (effective reasoning time: 1722ms)
% 5.32/3.03 % 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)>
% 5.32/3.03 % Axioms used in derivation (0):
% 5.32/3.03 % No. of inferences in proof: 18
% 5.32/3.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2623 ms resp. 1722 ms w/o parsing
% 5.77/3.11 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.77/3.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------