%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU585^2 : 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 : n014.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 08:28:39 AM UTC 2026
% Result : Theorem 3.67s 2.18s
% Output : Refutation 3.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 8 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 39 ( 8 equ; 0 cnn)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 112 ( 2 ~; 0 |; 0 &; 66 @)
% ( 0 <=>; 44 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 2 ^; 32 !; 0 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(setadjoin_decl,type,
setadjoin: $i > $i > $i ).
thf(setunion_decl,type,
setunion: $i > $i ).
thf(setadjoinE_decl,type,
setadjoinE: $o ).
thf(setunionE_decl,type,
setunionE: $o ).
thf(uniqinunit_decl,type,
uniqinunit: $o ).
thf(binunion_decl,type,
binunion: $i > $i > $i ).
thf(setadjoinE_def,definition,
( setadjoinE
= ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ).
thf(setunionE_def,definition,
( setunionE
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) ) ) ) ).
thf(uniqinunit_def,definition,
( uniqinunit
= ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) ) ) ) ).
thf(binunion_def,definition,
( binunion
= ( ^ [A: $i,B: $i] : ( setunion @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) ) ) ).
thf(1,conjecture,
( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(2,negated_conjecture,
~ ( setadjoinE
=> ( setunionE
=> ( uniqinunit
=> ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( binunion @ A @ B ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i,B: $i,C: $i] :
( ( in @ C @ ( setadjoin @ A @ B ) )
=> ! [D: $o] :
( ( ( C = A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( setunion @ A ) )
=> ! [C: $o] :
( ! [D: $i] :
( ( in @ B @ D )
=> ( ( in @ D @ A )
=> C ) )
=> C ) )
=> ( ! [A: $i,B: $i] :
( ( in @ A @ ( setadjoin @ B @ emptyset ) )
=> ( A = B ) )
=> ! [A: $i,B: $i,C: $i,D: $o] :
( ( in @ C @ ( setunion @ ( setadjoin @ A @ ( setadjoin @ B @ emptyset ) ) ) )
=> ( ( ( in @ C @ A )
=> D )
=> ( ( ( in @ C @ B )
=> D )
=> D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(26,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU585^2 : 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
% 0.10/0.20 % Computer : n014.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 13:52:30 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 ...
% 1.24/0.99 % [INFO] Parsing done (196ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 2.06/1.41 % [INFO] eprover registered as external prover.
% 2.06/1.42 % [INFO] Scanning for conjecture ...
% 2.24/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.24/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.24/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.24/1.58 % [INFO] Type checking passed.
% 2.24/1.59 % [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 ...
% 3.67/2.18 % External prover 'e' found a proof!
% 3.67/2.18 % [INFO] Killing All external provers ...
% 3.67/2.18 % Time passed: 1836ms (effective reasoning time: 1169ms)
% 3.67/2.18 % 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)>
% 3.67/2.18 % Axioms used in derivation (0):
% 3.67/2.18 % No. of inferences in proof: 4
% 3.67/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1836 ms resp. 1169 ms w/o parsing
% 3.90/2.23 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.90/2.23 % [INFO] Killing All external provers ...
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