%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 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 : n026.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 : Sun Sep 27 08:37:49 AM UTC 2026
% Result : Theorem 5.38s 3.45s
% Output : Refutation 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 6
% Syntax : Number of formulae : 14 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 30 ( 14 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 58 ( 4 ~; 7 |; 2 &; 38 @)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 0 ^; 13 !; 4 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
thf(subset_decl,type,
subset: $i > $i > $o ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(empty_set_decl,type,
empty_set: $i ).
thf(empty_decl,type,
empty: $i > $o ).
thf(6,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(24,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(4,axiom,
empty_set @ empty,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
thf(21,plain,
empty_set @ empty,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t39_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(8,plain,
~ ! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i] : ( A @ ( A @ subset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
thf(19,plain,
! [A: $i] : ( A @ ( A @ subset ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(22,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ singleton @ ( A @ subset ) )
<=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_zfmisc_1) ).
thf(27,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) )
=> ( B @ singleton @ ( A @ subset ) ) )
& ( ( B @ singleton @ ( A @ subset ) )
=> ( ( A
= ( B @ singleton ) )
| ( A = empty_set ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(44,plain,
$false,
inference(e,[status(thm)],[24,21,8,19,22,27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU160+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.23/0.50 % Computer : n026.cluster.edu
% 0.23/0.50 % Model : x86_64 x86_64
% 0.23/0.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.50 % Memory : 8046.5625MB
% 0.23/0.50 % OS : Linux 6.8.0-71-generic
% 0.23/0.50 % CPULimit : 300
% 0.23/0.50 % WCLimit : 300
% 0.23/0.50 % DateTime : Sat Sep 26 08:45:11 UTC 2026
% 0.23/0.50 % CPUTime :
% 0.23/0.50 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
% 1.49/1.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.81/1.68 % [INFO] Parsing done (275ms).
% 1.99/1.70 % [INFO] Running in sequential loop mode.
% 2.67/2.28 % [INFO] eprover registered as external prover.
% 2.67/2.29 % [INFO] Scanning for conjecture ...
% 3.06/2.43 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 3.06/2.49 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 3.23/2.50 % [INFO] Problem is first-order (TPTP FOF).
% 3.23/2.50 % [INFO] Type checking passed.
% 3.23/2.51 % [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 ...
% 5.38/3.44 % External prover 'e' found a proof!
% 5.38/3.44 % [INFO] Killing All external provers ...
% 5.38/3.44 % Time passed: 2725ms (effective reasoning time: 1735ms)
% 5.38/3.44 % 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)>
% 5.38/3.45 % Axioms used in derivation (5): fc1_xboole_0, l4_zfmisc_1, reflexivity_r1_tarski, rc1_xboole_0, rc2_xboole_0
% 5.38/3.45 % No. of inferences in proof: 14
% 5.38/3.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2725 ms resp. 1735 ms w/o parsing
% 5.63/3.51 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.63/3.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------