%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 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 : n002.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 08:31:20 AM UTC 2026
% Result : Theorem 3.56s 2.30s
% Output : Refutation 3.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 7 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 13 ~; 0 |; 2 &; 54 @)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 14 !; 4 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(set_difference_decl,type,
set_difference: $i > $i > $i ).
thf(singleton_decl,type,
singleton: $i > $i ).
thf(in_decl,type,
in: $i > $i > $o ).
thf(empty_decl,type,
empty: $i > $o ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
<=> ~ ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l34_zfmisc_1) ).
thf(24,plain,
! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) ) )
& ( ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
=> ~ ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
? [A: $i] :
~ ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
thf(21,plain,
? [A: $i] :
~ ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ in ) )
=> ~ ( A @ ( B @ in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
<=> ~ ( B @ ( A @ in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t67_zfmisc_1) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
<=> ~ ( B @ ( A @ in ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(7,plain,
~ ! [A: $i,B: $i] :
( ( ~ ( B @ ( A @ in ) )
=> ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) ) )
& ( ( ( B @ ( A @ singleton @ set_difference ) )
= ( A @ singleton ) )
=> ~ ( B @ ( A @ in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,axiom,
? [A: $i] : ( A @ empty ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
thf(19,plain,
? [A: $i] : ( A @ empty ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
$false,
inference(e,[status(thm)],[24,21,17,7,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET924+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % 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
% 0.12/0.39 % Computer : n002.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 08:28:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 0.89/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.17 % [INFO] Parsing done (177ms).
% 1.27/1.18 % [INFO] Running in sequential loop mode.
% 1.83/1.59 % [INFO] eprover registered as external prover.
% 2.02/1.60 % [INFO] Scanning for conjecture ...
% 2.02/1.69 % [INFO] Found a conjecture (or negated_conjecture) and 4 axioms. Running axiom selection ...
% 2.20/1.73 % [INFO] Axiom selection finished. Selected 4 axioms (removed 0 axioms).
% 2.20/1.74 % [INFO] Problem is first-order (TPTP FOF).
% 2.20/1.74 % [INFO] Type checking passed.
% 2.20/1.75 % [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 ...
% 3.56/2.30 % External prover 'e' found a proof!
% 3.56/2.30 % [INFO] Killing All external provers ...
% 3.56/2.30 % Time passed: 1760ms (effective reasoning time: 1113ms)
% 3.56/2.30 % 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)>
% 3.56/2.30 % Axioms used in derivation (4): l34_zfmisc_1, rc2_xboole_0, antisymmetry_r2_hidden, rc1_xboole_0
% 3.56/2.30 % No. of inferences in proof: 12
% 3.56/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1760 ms resp. 1113 ms w/o parsing
% 3.56/2.34 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.56/2.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------