%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO286^5 : 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 : n005.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 08:45:32 AM UTC 2026
% Result : Theorem 4.39s 2.50s
% Output : Refutation 4.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 4 unt; 0 typ; 1 def)
% Number of atoms : 13 ( 1 equ; 0 cnn)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 28 ( 5 ~; 0 |; 2 &; 15 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 4 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 ^; 5 !; 3 ?; 9 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(y_decl,type,
y: $i ).
thf(cQ_decl,type,
cQ: $i > $o ).
thf(cR_decl,type,
cR: $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] : ( cR @ A ) ) ) ).
thf(1,conjecture,
( ! [A: $i > $o] : ( A @ y )
=> ( ? [A: $i] : ( cR @ A )
=> ( cQ @ y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTEST1) ).
thf(2,negated_conjecture,
~ ( ! [A: $i > $o] : ( A @ y )
=> ( ? [A: $i] : ( cR @ A )
=> ( cQ @ y ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ! [A: $i > $o] : ( A @ y )
=> ( ? [A: $i] : ( cR @ A )
=> ( cQ @ y ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [A: $i > $o] :
( ( A @ y )
& ( cR @ sk1 )
& ~ ( cQ @ y ) ),
inference(cnf,[status(esa)],[3]) ).
thf(7,plain,
~ ( cQ @ y ),
inference(cnfConj,[status(thm)],[4]) ).
thf(5,plain,
! [A: $i > $o] : ( A @ y ),
inference(cnfConj,[status(thm)],[4]) ).
thf(9,plain,
~ $true,
inference(rewrite,[status(thm)],[7,5]) ).
thf(10,plain,
$false,
inference(simp,[status(thm)],[9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO286^5 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.11/0.21 % Computer : n005.cluster.edu
% 0.11/0.21 % Model : x86_64 x86_64
% 0.11/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.21 % Memory : 8046.5625MB
% 0.11/0.21 % OS : Linux 6.8.0-71-generic
% 0.11/0.21 % CPULimit : 300
% 0.11/0.21 % WCLimit : 300
% 0.11/0.21 % DateTime : Tue Sep 29 16:43:01 UTC 2026
% 0.11/0.21 % CPUTime :
% 0.11/0.21 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
% 1.19/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.70/1.29 % [INFO] Parsing done (252ms).
% 1.91/1.31 % [INFO] Running in sequential loop mode.
% 2.64/1.85 % [INFO] eprover registered as external prover.
% 2.64/1.86 % [INFO] Scanning for conjecture ...
% 2.88/1.94 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.88/1.97 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.88/1.97 % [INFO] Problem is higher-order (TPTP THF).
% 2.88/1.98 % [INFO] Type checking passed.
% 2.88/1.98 % [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 ...
% 3.96/2.49 % [INFO] Killing All external provers ...
% 3.96/2.50 % Time passed: 2081ms (effective reasoning time: 1176ms)
% 3.96/2.50 % 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)>
% 3.96/2.50 % Axioms used in derivation (0):
% 3.96/2.50 % No. of inferences in proof: 8
% 4.39/2.50 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2081 ms resp. 1176 ms w/o parsing
% 4.39/2.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.39/2.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------