%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM564+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n019.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 08:09:10 AM UTC 2026
% Result : Theorem 6.91s 2.48s
% Output : Refutation 7.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 31 ( 1 equ; 0 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 92 ( 11 ~; 6 |; 8 &; 60 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 9 ( 0 ^; 5 !; 3 ?; 9 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(slcrc0_decl,type,
slcrc0: $i ).
thf(aSet0_decl,type,
aSet0: $i > $o ).
thf(aElementOf0_decl,type,
aElementOf0: $i > $i > $o ).
thf(aSubsetOf0_decl,type,
aSubsetOf0: $i > $i > $o ).
thf(slbdtsldtrb0_decl,type,
slbdtsldtrb0: $i > $i > $i ).
thf(xS_decl,type,
xS: $i ).
thf(sz00_decl,type,
sz00: $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( slcrc0 @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ) ).
thf(1,conjecture,
( ( ~ ? [A: $i] : ( slcrc0 @ ( A @ aElementOf0 ) )
& ( slcrc0 @ aSet0 ) )
=> ( ( sz00 @ ( xS @ slbdtsldtrb0 ) @ ( slcrc0 @ aElementOf0 ) )
| ( xS @ ( slcrc0 @ aSubsetOf0 ) )
| ! [A: $i] :
( ( slcrc0 @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
thf(2,negated_conjecture,
~ ( ( ~ ? [A: $i] : ( slcrc0 @ ( A @ aElementOf0 ) )
& ( slcrc0 @ aSet0 ) )
=> ( ( sz00 @ ( xS @ slbdtsldtrb0 ) @ ( slcrc0 @ aElementOf0 ) )
| ( xS @ ( slcrc0 @ aSubsetOf0 ) )
| ! [A: $i] :
( ( slcrc0 @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(81,plain,
~ ( ( ~ ? [A: $i] : ( slcrc0 @ ( A @ aElementOf0 ) )
& ( slcrc0 @ aSet0 ) )
=> ( ( sz00 @ ( xS @ slbdtsldtrb0 ) @ ( slcrc0 @ aElementOf0 ) )
| ( xS @ ( slcrc0 @ aSubsetOf0 ) )
| ! [A: $i] :
( ( slcrc0 @ ( A @ aElementOf0 ) )
=> ( xS @ ( A @ aElementOf0 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(82,plain,
! [A: $i] :
( ~ ( sz00 @ ( xS @ slbdtsldtrb0 ) @ ( slcrc0 @ aElementOf0 ) )
& ~ ( xS @ ( slcrc0 @ aSubsetOf0 ) )
& ~ ( xS @ ( sk1 @ aElementOf0 ) )
& ( slcrc0 @ ( sk1 @ aElementOf0 ) )
& ~ ( slcrc0 @ ( A @ aElementOf0 ) )
& ( slcrc0 @ aSet0 ) ),
inference(cnf,[status(esa)],[81]) ).
thf(83,plain,
slcrc0 @ ( sk1 @ aElementOf0 ),
inference(cnfConj,[status(thm)],[82]) ).
thf(88,plain,
! [A: $i] :
~ ( slcrc0 @ ( A @ aElementOf0 ) ),
inference(cnfConj,[status(thm)],[82]) ).
thf(632,plain,
$false,
inference(rewrite,[status(thm)],[83,88]) ).
thf(633,plain,
$false,
inference(simp,[status(thm)],[632]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : NUM564+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % 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
% 0.23/0.50 % Computer : n019.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 03:14:50 UTC 2026
% 0.23/0.51 % CPUTime :
% 0.23/0.51 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
% 0.77/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.01/0.98 % [INFO] Parsing done (149ms).
% 1.01/0.98 % [INFO] Running in sequential loop mode.
% 1.84/1.18 % [INFO] eprover registered as external prover.
% 1.84/1.19 % [INFO] Scanning for conjecture ...
% 2.04/1.22 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.23 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.24 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.25 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.26 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.27 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.04/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 78 axioms. Running axiom selection ...
% 2.31/1.35 % [INFO] Axiom selection finished. Selected 78 axioms (removed 0 axioms).
% 2.31/1.35 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.39 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.31/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.67/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.67/1.40 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.67/1.41 % [INFO] Definitions in FOF are currently treated as axioms.
% 2.67/1.41 % [INFO] Problem is first-order (TPTP FOF).
% 2.67/1.42 % [INFO] Type checking passed.
% 2.67/1.43 % [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 ...
% 6.91/2.47 % [INFO] Killing All external provers ...
% 6.91/2.48 % Time passed: 1857ms (effective reasoning time: 1487ms)
% 6.91/2.48 % 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)>
% 6.91/2.48 % Axioms used in derivation (0):
% 6.91/2.48 % No. of inferences in proof: 8
% 6.91/2.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1857 ms resp. 1487 ms w/o parsing
% 7.45/2.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.45/2.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------