%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n011.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 08:46:07 AM UTC 2026
% Result : Theorem 4.01s 2.42s
% Output : Refutation 4.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO559^1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % 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
% 0.10/0.21 % Computer : n011.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.21 % CPULimit : 300
% 0.10/0.21 % WCLimit : 300
% 0.10/0.21 % DateTime : Tue Sep 29 17:15:01 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 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
% 0.89/0.78 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (186ms).
% 1.20/0.99 % [INFO] Running in sequential loop mode.
% 1.76/1.37 % [INFO] eprover registered as external prover.
% 1.76/1.38 % [INFO] Scanning for conjecture ...
% 1.94/1.46 % [INFO] Found a conjecture (or negated_conjecture) and 2 axioms. Running axiom selection ...
% 1.94/1.49 % [INFO] Axiom selection finished. Selected 2 axioms (removed 0 axioms).
% 2.11/1.50 % [INFO] Problem is higher-order (TPTP THF).
% 2.11/1.51 % [INFO] Type checking passed.
% 2.11/1.51 % [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 ...
% 4.01/2.41 % [INFO] Killing All external provers ...
% 4.01/2.41 % Time passed: 2059ms (effective reasoning time: 1417ms)
% 4.01/2.41 % 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)>
% 4.01/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2059 ms resp. 1417 ms w/o parsing
% 4.01/2.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.01/2.47 thf(epso_decl, type, epso: (($o > $o) > $o)).
% 4.01/2.47 thf(epsoo_decl, type, epsoo: ((($o > $o) > $o) > ($o > $o))).
% 4.01/2.47 thf(sk2_decl, type, sk2: $o).
% 4.01/2.47 thf(3,axiom,((! [A:($o > $o)]: ((? [B:$o]: (A @ B)) => (A @ (epso @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',choiceaxo)).
% 4.01/2.47 thf(9,plain,((! [A:($o > $o)]: ((? [B:$o]: (A @ B)) => (A @ (epso @ (A)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.01/2.47 thf(12,plain,(((($true)) => (epso @ (^ [A:$o]: (A))))),inference(instance,[status(thm)],[9])).
% 4.01/2.47 thf(13,plain,((epso @ (^ [A:$o]: (A)))),inference(simp,[status(thm)],[12])).
% 4.01/2.47 thf(28,axiom,((? [A:((($o > $o) > $o) > ($o > $o))]: ! [B:(($o > $o) > $o)]: ((? [C:($o > $o)]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 4.01/2.47 thf(29,plain,(! [A:($o > $o)] : ((~ (epso @ (A))) | (epso @ (epsoo @ (epso))))),inference(choice,[status(esa)],[28])).
% 4.01/2.47 thf(14,plain,(((~ (($false))) => (~ (epso @ ((~)))))),inference(instance,[status(thm)],[9])).
% 4.01/2.47 thf(15,plain,((~ (epso @ ((~))))),inference(simp,[status(thm)],[14])).
% 4.01/2.47 thf(40,plain,(! [A:($o > $o)] : ((~ (epso @ (A))) | ~ (($true)) | ((epso @ (epsoo @ (epso))) != (epso @ ((~)))))),inference(paramod_ordered,[status(thm)],[29,15])).
% 4.01/2.47 thf(41,plain,(! [A:($o > $o)] : ((~ (epso @ (A))) | ((epso @ (epsoo @ (epso))) != (epso @ ((~)))))),inference(simp,[status(thm)],[40])).
% 4.01/2.47 thf(42,plain,(! [A:($o > $o)] : ((~ (epso @ (A))) | ((epsoo @ (epso)) != ((~))))),inference(simp,[status(thm)],[41])).
% 4.01/2.47 thf(47,plain,(! [A:($o > $o)] : (~ (($true)) | ((epsoo @ (epso)) != ((~))) | ((epso @ (^ [B:$o]: (B))) != (epso @ (A))))),inference(paramod_ordered,[status(thm)],[13,42])).
% 4.01/2.47 thf(48,plain,(! [A:($o > $o)] : (((epsoo @ (epso)) != ((~))) | ((epso @ (^ [B:$o]: (B))) != (epso @ (A))))),inference(simp,[status(thm)],[47])).
% 4.01/2.47 thf(49,plain,(((epsoo @ (epso)) != ((~)))),inference(pattern_uni,[status(thm)],[48:[bind(A, $thf(^ [B:$o]: (B)))]])).
% 4.01/2.47 thf(56,plain,(((epsoo @ (epso) @ sk2) != (~ (sk2)))),inference(func_ext,[status(esa)],[49])).
% 4.01/2.47 thf(1,conjecture,(((epsoo @ epso @ ($false)) => (epsoo @ epso @ ($true)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c)).
% 4.01/2.47 thf(2,negated_conjecture,((~ ((epsoo @ epso @ ($false)) => (epsoo @ epso @ ($true))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.01/2.47 thf(5,plain,((~ ((epsoo @ (epso) @ ($false)) => (epsoo @ (epso) @ ($true))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.01/2.47 thf(6,plain,(((epsoo @ (epso) @ ($false)) & ~ (epsoo @ (epso) @ ($true)))),inference(cnf,[status(esa)],[5])).
% 4.01/2.47 thf(7,plain,((epsoo @ (epso) @ ($false))),inference(cnfConj,[status(thm)],[6])).
% 4.01/2.47 thf(73,plain,((~ (~ (sk2))) | ((epsoo @ (epso) @ sk2) != (epsoo @ (epso) @ ($false)))),inference(paramod_ordered,[status(thm)],[7,56])).
% 4.01/2.47 thf(74,plain,(sk2 | ((epsoo @ (epso) @ sk2) != (epsoo @ (epso) @ ($false)))),inference(simp,[status(thm)],[73])).
% 4.01/2.47 thf(75,plain,(sk2 | ((epso) != (epso)) | sk2),inference(simp,[status(thm)],[74])).
% 4.01/2.47 thf(78,plain,(sk2),inference(simp,[status(thm)],[75])).
% 4.01/2.47 thf(79,plain,(((epsoo @ (epso) @ ($true)) != (~ (($true))))),inference(rewrite,[status(thm)],[56,78])).
% 4.01/2.47 thf(80,plain,((epsoo @ (epso) @ ($true))),inference(simp,[status(thm)],[79])).
% 4.01/2.47 thf(8,plain,((~ (epsoo @ (epso) @ ($true)))),inference(cnfConj,[status(thm)],[6])).
% 4.01/2.47 thf(81,plain,(($false)),inference(rewrite,[status(thm)],[80,8])).
% 4.01/2.47 thf(82,plain,(($false)),inference(simp,[status(thm)],[81])).
% 4.01/2.47 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.01/2.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------