%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SYO558^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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 : 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 4.04s 2.45s
% Output : Refutation 4.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO558^1 : TPTP v9.3.1. Bugfixed v7.5.0.
% 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
% 0.10/0.20 % Computer : n011.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 17:15:01 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 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
% 0.87/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.19/0.97 % [INFO] Parsing done (187ms).
% 1.19/0.98 % [INFO] Running in sequential loop mode.
% 1.76/1.37 % [INFO] eprover registered as external prover.
% 1.76/1.38 % [INFO] Scanning for conjecture ...
% 1.94/1.47 % [INFO] Found a conjecture (or negated_conjecture) and 1 axioms. Running axiom selection ...
% 2.10/1.50 % [INFO] Axiom selection finished. Selected 1 axioms (removed 0 axioms).
% 2.10/1.51 % [INFO] Problem is higher-order (TPTP THF).
% 2.10/1.51 % [INFO] Type checking passed.
% 2.10/1.52 % [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 ...
% 4.04/2.44 % [INFO] Killing All external provers ...
% 4.04/2.45 % Time passed: 2099ms (effective reasoning time: 1454ms)
% 4.04/2.45 % 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)>
% 4.04/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2099 ms resp. 1454 ms w/o parsing
% 4.04/2.49 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.04/2.49 thf(eps_decl, type, eps: (($i > $o) > $i)).
% 4.04/2.49 thf(sk1_decl, type, sk1: ($i > $o)).
% 4.04/2.49 thf(sk2_decl, type, sk2: $i).
% 4.04/2.49 thf(sk2_def, definition, sk2 = (@+ [A:$i]: ~ (sk1 @ A)) ).
% 4.04/2.49 thf(1,conjecture,(((^ [A:($i > $o)]: (A @ (eps @ (^ [B:$i]: ~ (A @ B))))) = ((!) @ $i))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 4.04/2.49 thf(2,negated_conjecture,((~ ((^ [A:($i > $o)]: (A @ (eps @ (^ [B:$i]: ~ (A @ B))))) = ((!) @ $i)))),inference(neg_conjecture,[status(cth)],[1])).
% 4.04/2.49 thf(4,plain,((~ ((^ [A:($i > $o)]: (A @ (eps @ (^ [B:$i]: ~ (A @ B))))) = ((!) @ $i)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.04/2.49 thf(5,plain,(((^ [A:($i > $o)]: (A @ (eps @ (^ [B:$i]: ~ (A @ B))))) != ((!) @ $i))),inference(lifteq,[status(thm)],[4])).
% 4.04/2.49 thf(9,plain,(((sk1 @ (eps @ (^ [A:$i]: ~ (sk1 @ A)))) != (! [A:$i]: (sk1 @ A)))),inference(func_ext,[status(esa)],[5])).
% 4.04/2.49 thf(10,plain,((~ (sk1 @ (eps @ (^ [A:$i]: ~ (sk1 @ A))))) | (~ (! [A:$i]: (sk1 @ A)))),inference(bool_ext,[status(thm)],[9])).
% 4.04/2.49 thf(14,plain,((~ (sk1 @ (eps @ (^ [A:$i]: ~ (sk1 @ A))))) | (~ (sk1 @ sk2))),inference(cnf,[status(esa)],[10])).
% 4.04/2.49 thf(11,plain,((sk1 @ (eps @ (^ [A:$i]: ~ (sk1 @ A)))) | (! [A:$i]: (sk1 @ A))),inference(bool_ext,[status(thm)],[9])).
% 4.04/2.49 thf(15,plain,(! [A:$i] : ((sk1 @ (eps @ (^ [B:$i]: ~ (sk1 @ B)))) | (sk1 @ A))),inference(cnf,[status(esa)],[11])).
% 4.04/2.49 thf(68,plain,(! [A:$i] : ((sk1 @ (eps @ (^ [B:$i]: ~ (sk1 @ B)))) | ((sk1 @ A) != (sk1 @ (eps @ (^ [B:$i]: ~ (sk1 @ B))))) | ~ (($true)))),inference(eqfactor_ordered,[status(thm)],[15])).
% 4.04/2.49 thf(74,plain,((sk1 @ (eps @ (^ [A:$i]: ~ (sk1 @ A))))),inference(pattern_uni,[status(thm)],[68:[bind(A, $thf(eps @ (^ [B:$i]: ~ (sk1 @ B))))]])).
% 4.04/2.49 thf(80,plain,(~ (($true)) | (~ (sk1 @ sk2))),inference(rewrite,[status(thm)],[14,74])).
% 4.04/2.49 thf(81,plain,((~ (sk1 @ sk2))),inference(simp,[status(thm)],[80])).
% 4.04/2.49 thf(12,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 4.04/2.49 thf(13,plain,(! [A:$i] : ((~ (~ (sk1 @ A))) | (~ (sk1 @ (eps @ (^ [B:$i]: ~ (sk1 @ B))))))),inference(choice,[status(esa)],[12])).
% 4.04/2.49 thf(16,plain,(! [A:$i] : ((sk1 @ A) | (~ (sk1 @ (eps @ (^ [B:$i]: ~ (sk1 @ B))))))),inference(cnf,[status(esa)],[13])).
% 4.04/2.49 thf(85,plain,(! [A:$i] : ((sk1 @ A) | ~ (($true)))),inference(rewrite,[status(thm)],[16,74])).
% 4.04/2.49 thf(86,plain,(! [A:$i] : ((sk1 @ A))),inference(simp,[status(thm)],[85])).
% 4.04/2.49 thf(103,plain,(~ (($true))),inference(rewrite,[status(thm)],[81,86])).
% 4.04/2.49 thf(104,plain,(($false)),inference(simp,[status(thm)],[103])).
% 4.04/2.49 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.04/2.49 % [INFO] Killing All external provers ...
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