%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU541^2 : 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 : n016.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 08:28:28 AM UTC 2026
% Result : Theorem 2.59s 1.71s
% Output : Refutation 2.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 6 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 12 ( 2 equ; 0 cnn)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 15 ( 2 ~; 0 |; 0 &; 8 @)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(prop2set_decl,type,
prop2set: $o > $i ).
thf(prop2setI_decl,type,
prop2setI: $o ).
thf(set2prop_decl,type,
set2prop: $i > $o ).
thf(prop2setI_def,definition,
( prop2setI
= ( ! [A: $o] :
( A
=> ( in @ emptyset @ ( prop2set @ A ) ) ) ) ) ).
thf(set2prop_def,definition,
( set2prop
= ( in @ emptyset ) ) ).
thf(1,conjecture,
( prop2setI
=> ! [A: $o] :
( A
=> ( set2prop @ ( prop2set @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(2,negated_conjecture,
~ ( prop2setI
=> ! [A: $o] :
( A
=> ( set2prop @ ( prop2set @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ $true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
$false,
inference(simp,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU541^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.09 % 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
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:54:04 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 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
% 1.05/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.99 % [INFO] Parsing done (192ms).
% 1.25/1.01 % [INFO] Running in sequential loop mode.
% 2.03/1.42 % [INFO] eprover registered as external prover.
% 2.03/1.43 % [INFO] Scanning for conjecture ...
% 2.21/1.53 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.21/1.56 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.21/1.56 % [INFO] Problem is higher-order (TPTP THF).
% 2.21/1.56 % [INFO] Type checking passed.
% 2.21/1.57 % [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 ...
% 2.59/1.70 % [INFO] Killing All external provers ...
% 2.59/1.71 % Time passed: 1343ms (effective reasoning time: 688ms)
% 2.59/1.71 % 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)>
% 2.59/1.71 % Axioms used in derivation (0):
% 2.59/1.71 % No. of inferences in proof: 4
% 2.59/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1343 ms resp. 688 ms w/o parsing
% 2.59/1.76 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.59/1.76 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------