%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU513^2 : 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 : n019.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 08:28:21 AM UTC 2026
% Result : Theorem 2.82s 2.00s
% Output : Refutation 3.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 15 ( 1 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 45 ( 5 ~; 0 |; 1 &; 36 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 8 ( 0 ^; 8 !; 0 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setadjoinIL_decl,type,
setadjoinIL: $o ).
thf(setadjoinIL_def,definition,
( setadjoinIL
= ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) ) ) ) ).
thf(1,conjecture,
( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(2,negated_conjecture,
~ ( setadjoinIL
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i] : ( in @ A @ ( setadjoin @ A @ B ) )
=> ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i,A: $i] :
( ( in @ A @ ( setadjoin @ A @ B ) )
& ~ ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(6,plain,
~ ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [B: $i,A: $i] : ( in @ A @ ( setadjoin @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(7,plain,
~ $true,
inference(rewrite,[status(thm)],[6,5]) ).
thf(8,plain,
$false,
inference(simp,[status(thm)],[7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU513^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.07 % 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
% 0.10/0.19 % Computer : n019.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:47:33 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (175ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.75/1.36 % [INFO] eprover registered as external prover.
% 1.75/1.37 % [INFO] Scanning for conjecture ...
% 1.92/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.50 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.50 % [INFO] Type checking passed.
% 2.08/1.51 % [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 ...
% 2.82/1.99 % [INFO] Killing All external provers ...
% 2.82/2.00 % Time passed: 1649ms (effective reasoning time: 1009ms)
% 2.82/2.00 % 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)>
% 2.82/2.00 % Axioms used in derivation (0):
% 2.82/2.00 % No. of inferences in proof: 8
% 2.82/2.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1649 ms resp. 1009 ms w/o parsing
% 3.11/2.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.11/2.04 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------