%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU510^2 : 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 : n007.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 3.47s 2.11s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 7 ( 4 unt; 0 typ; 3 def)
% Number of atoms : 24 ( 5 equ; 0 cnn)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 57 ( 4 ~; 0 |; 0 &; 35 @)
% ( 0 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 1 ^; 19 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_decl,type,
dsetconstrI: $o ).
thf(emptysetE_decl,type,
emptysetE: $o ).
thf(nonempty_decl,type,
nonempty: $i > $o ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(emptysetE_def,definition,
( emptysetE
= ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B ) ) ) ).
thf(nonempty_def,definition,
( nonempty
= ( ^ [A: $i] : ( A != emptyset ) ) ) ).
thf(1,conjecture,
( dsetconstrI
=> ( emptysetE
=> ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( nonempty @ ( dsetconstr @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(2,negated_conjecture,
~ ( dsetconstrI
=> ( emptysetE
=> ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( nonempty @ ( dsetconstr @ A @ B ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) )
=> ( ! [A: $i] :
( ( in @ A @ emptyset )
=> ! [B: $o] : B )
=> ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( ( dsetconstr @ A @ B )
!= emptyset ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(13,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU510^2 : 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
% 0.11/0.22 % Computer : n007.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 13:45:11 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 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
% 0.89/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.98 % [INFO] Parsing done (189ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.06/1.41 % [INFO] eprover registered as external prover.
% 2.06/1.41 % [INFO] Scanning for conjecture ...
% 2.26/1.52 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.26/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.26/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.26/1.56 % [INFO] Type checking passed.
% 2.26/1.57 % [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 ...
% 3.47/2.11 % External prover 'e' found a proof!
% 3.47/2.11 % [INFO] Killing All external provers ...
% 3.47/2.11 % Time passed: 1742ms (effective reasoning time: 1102ms)
% 3.47/2.11 % 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)>
% 3.47/2.11 % Axioms used in derivation (0):
% 3.47/2.11 % No. of inferences in proof: 4
% 3.47/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1742 ms resp. 1102 ms w/o parsing
% 3.77/2.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.77/2.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------