%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU511^2 : TPTP v9.3.1. Released v3.7.0.
% 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 : n009.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 08:28:20 AM UTC 2026
% Result : Theorem 3.83s 2.20s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 20 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 40 ( 13 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 70 ( 13 ~; 5 |; 2 &; 38 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 6 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 1 ^; 19 !; 6 ?; 28 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(nonempty_decl,type,
nonempty: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] : ( in @ A @ sk1 ) ) ) ).
thf(1,conjecture,
( emptysetE
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( nonempty @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(2,negated_conjecture,
~ ( emptysetE
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( nonempty @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ? [A: $i] : ( in @ A @ emptyset )
=> ! [A: $o] : A )
=> ! [A: $i] :
( ? [B: $i] : ( in @ B @ A )
=> ( A != emptyset ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(5,plain,
! [B: $o,A: $i] :
( ( ~ ( in @ A @ emptyset )
| B )
& ( in @ sk2 @ sk1 )
& ( sk1 = emptyset ) ),
inference(cnf,[status(esa)],[4]) ).
thf(7,plain,
in @ sk2 @ sk1,
inference(cnfConj,[status(thm)],[5]) ).
thf(8,plain,
sk1 = emptyset,
inference(cnfConj,[status(thm)],[5]) ).
thf(9,plain,
sk1 = emptyset,
inference(lifteq,[status(thm)],[8]) ).
thf(10,plain,
in @ sk2 @ emptyset,
inference(rewrite,[status(thm)],[7,9]) ).
thf(6,plain,
! [B: $o,A: $i] :
( ~ ( in @ A @ emptyset )
| B ),
inference(cnfConj,[status(thm)],[5]) ).
thf(14,plain,
! [B: $o,A: $i] :
( ~ $true
| B
| ( ( in @ sk2 @ emptyset )
!= ( in @ A @ emptyset ) ) ),
inference(paramod_ordered,[status(thm)],[10,6]) ).
thf(15,plain,
! [B: $o,A: $i] :
( B
| ( ( in @ sk2 @ emptyset )
!= ( in @ A @ emptyset ) ) ),
inference(simp,[status(thm)],[14]) ).
thf(16,plain,
! [A: $o] : A,
inference(pattern_uni,[status(thm)],[15:[bind(A,$thf( sk2 ))]]) ).
thf(24,plain,
! [A: $o] : A,
inference(simp,[status(thm)],[16]) ).
thf(37,plain,
$false,
inference(prim_subst,[status(thm)],[24:[bind(A,$thf( $false ))]]) ).
thf(43,plain,
$false,
inference(simp,[status(thm)],[37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU511^2 : TPTP v9.3.1. Released v3.7.0.
% 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
% 0.11/0.22 % Computer : n009.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 13:47:30 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 1.00/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.98 % [INFO] Parsing done (176ms).
% 1.19/0.99 % [INFO] Running in sequential loop mode.
% 1.77/1.39 % [INFO] eprover registered as external prover.
% 1.96/1.40 % [INFO] Scanning for conjecture ...
% 2.14/1.50 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.14/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.14/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.14/1.54 % [INFO] Type checking passed.
% 2.14/1.54 % [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 ...
% 3.65/2.19 % [INFO] Killing All external provers ...
% 3.83/2.20 % Time passed: 1822ms (effective reasoning time: 1198ms)
% 3.83/2.20 % 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)>
% 3.83/2.20 % Axioms used in derivation (0):
% 3.83/2.20 % No. of inferences in proof: 16
% 3.83/2.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1822 ms resp. 1198 ms w/o parsing
% 3.83/2.25 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.83/2.25 % [INFO] Killing All external provers ...
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