%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU540^2 : 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 : n004.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 3.29s 2.11s
% Output : Refutation 3.53s
% 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 : 23 ( 3 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 61 ( 2 ~; 0 |; 0 &; 42 @)
% ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 3 ^; 15 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_decl,type,
in: $i > $i > $o ).
thf(emptyset_decl,type,
emptyset: $i ).
thf(powerset_decl,type,
powerset: $i > $i ).
thf(dsetconstr_decl,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(dsetconstrI_decl,type,
dsetconstrI: $o ).
thf(prop2set_decl,type,
prop2set: $o > $i ).
thf(powersetI_decl,type,
powersetI: $o ).
thf(dsetconstrI_def,definition,
( dsetconstrI
= ( ! [A: $i,B: $i > $o,C: $i] :
( ( in @ C @ A )
=> ( ( B @ C )
=> ( in @ C @ ( dsetconstr @ A @ B ) ) ) ) ) ) ).
thf(prop2set_def,definition,
( prop2set
= ( ^ [A: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [B: $i] : A ) ) ) ).
thf(powersetI_def,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ) ).
thf(1,conjecture,
( dsetconstrI
=> ( powersetI
=> ! [A: $o] :
( A
=> ( in @ emptyset @ ( prop2set @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(2,negated_conjecture,
~ ( dsetconstrI
=> ( powersetI
=> ! [A: $o] :
( A
=> ( in @ emptyset @ ( prop2set @ A ) ) ) ) ),
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,B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ( in @ C @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ! [A: $o] :
( A
=> ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [B: $i] : A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(12,plain,
$false,
inference(e,[status(thm)],[3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU540^2 : 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
% 0.10/0.22 % Computer : n004.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 13:48:52 UTC 2026
% 0.10/0.23 % CPUTime :
% 0.10/0.23 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
% 1.03/0.80 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.22/1.00 % [INFO] Parsing done (194ms).
% 1.22/1.01 % [INFO] Running in sequential loop mode.
% 2.02/1.42 % [INFO] eprover registered as external prover.
% 2.02/1.43 % [INFO] Scanning for conjecture ...
% 2.20/1.54 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.20/1.58 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.20/1.58 % [INFO] Problem is higher-order (TPTP THF).
% 2.20/1.58 % [INFO] Type checking passed.
% 2.20/1.59 % [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 ...
% 3.29/2.11 % External prover 'e' found a proof!
% 3.29/2.11 % [INFO] Killing All external provers ...
% 3.29/2.11 % Time passed: 1745ms (effective reasoning time: 1089ms)
% 3.29/2.11 % 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)>
% 3.29/2.11 % Axioms used in derivation (0):
% 3.29/2.11 % No. of inferences in proof: 4
% 3.29/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1745 ms resp. 1089 ms w/o parsing
% 3.53/2.15 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.53/2.15 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------