%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO086^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 : Wed Sep 30 08:45:12 AM UTC 2026
% Result : Theorem 3.04s 1.97s
% Output : Refutation 3.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 60 ( 0 equ; 0 cnn)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 80 ( 32 ~; 18 |; 24 &; 0 @)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 4 ( 3 usr; 4 con; 0-0 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(cR_decl,type,
cR: $o ).
thf(cQ_decl,type,
cQ: $o ).
thf(cP_decl,type,
cP: $o ).
thf(1,conjecture,
( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM50_11) ).
thf(2,negated_conjecture,
~ ( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ~ cP
& ( ( cQ
& ~ cR )
| ( ~ cQ
& cR ) ) )
=> ( ( ( cP
& cQ )
| ( ~ cP
& ~ cQ ) )
=> cR ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ~ cP
& ( cQ
| ~ cQ )
& ( cQ
| cR )
& ( ~ cR
| ~ cQ )
& ( ~ cR
| cR )
& ( cP
| ~ cP )
& ( cP
| ~ cQ )
& ( cQ
| ~ cP )
& ( cQ
| ~ cQ )
& ~ cR ),
inference(cnf,[status(esa)],[3]) ).
thf(9,plain,
( cQ
| cR ),
inference(cnfConj,[status(thm)],[4]) ).
thf(6,plain,
( cP
| ~ cQ ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
~ cP,
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
( $false
| ~ cQ ),
inference(rewrite,[status(thm)],[6,11]) ).
thf(16,plain,
~ cQ,
inference(simp,[status(thm)],[15]) ).
thf(13,plain,
~ cR,
inference(cnfConj,[status(thm)],[4]) ).
thf(19,plain,
( $false
| $false ),
inference(rewrite,[status(thm)],[9,16,13]) ).
thf(20,plain,
$false,
inference(simp,[status(thm)],[19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO086^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.09/0.21 % Computer : n002.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:36:08 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 1.05/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.99 % [INFO] Parsing done (177ms).
% 1.24/1.00 % [INFO] Running in sequential loop mode.
% 2.01/1.41 % [INFO] eprover registered as external prover.
% 2.01/1.42 % [INFO] Scanning for conjecture ...
% 2.01/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.53 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.53 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.53 % [INFO] Type checking passed.
% 2.19/1.54 % [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 ...
% 3.04/1.96 % [INFO] Killing All external provers ...
% 3.04/1.97 % Time passed: 1606ms (effective reasoning time: 960ms)
% 3.04/1.97 % 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)>
% 3.04/1.97 % Axioms used in derivation (0):
% 3.04/1.97 % No. of inferences in proof: 12
% 3.04/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1606 ms resp. 960 ms w/o parsing
% 3.04/2.00 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.04/2.00 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------