%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% 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 : n017.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 08:37:16 AM UTC 2026
% Result : Theorem 14.19s 4.13s
% Output : Refutation 12.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEV428^1 : TPTP v9.3.1. Released v5.2.0.
% 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
% 0.08/0.20 % Computer : n017.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 15:42:22 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 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
% 0.90/0.78 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (191ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 2.06/1.46 % [INFO] eprover registered as external prover.
% 2.06/1.47 % [INFO] Scanning for conjecture ...
% 2.32/1.57 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.51/1.61 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.51/1.62 % [INFO] Problem is higher-order (TPTP THF).
% 2.51/1.62 % [INFO] Type checking passed.
% 2.51/1.63 % [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 ...
% 14.19/4.12 % [INFO] Killing All external provers ...
% 14.19/4.12 % Time passed: 3771ms (effective reasoning time: 3121ms)
% 14.19/4.12 % 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)>
% 14.19/4.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3771 ms resp. 3121 ms w/o parsing
% 12.95/4.17 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.95/4.17 thf(eps_decl, type, eps: (($i > $o) > $i)).
% 12.95/4.17 thf(epsio_decl, type, epsio: ((($i > $o) > $o) > ($i > $o))).
% 12.95/4.17 thf(setunion_decl, type, setunion: ((($i > $o) > $o) > ($i > $o))).
% 12.95/4.17 thf(choosenonempty_decl, type, choosenonempty: ((($i > $o) > $o) > ($i > $o))).
% 12.95/4.17 thf(c_decl, type, c: (($i > $o) > $o)).
% 12.95/4.17 thf(a_decl, type, a: $i).
% 12.95/4.17 thf(sk1_decl, type, sk1: ($i > $o)).
% 12.95/4.17 thf(setunion_def, definition, setunion = (^ [A:(($i > $o) > $o),B:$i]: ? [C:($i > $o)]: ((A @ C) & (C @ B))) ).
% 12.95/4.17 thf(choosenonempty_def, definition, choosenonempty = (^ [A:(($i > $o) > $o)]: (epsio @ (^ [B:($i > $o)]: ((A @ B) & (B @ (eps @ B)))))) ).
% 12.95/4.17 thf(sk1_def, definition, sk1 = (@+ [A:($i > $o)]: ((c @ (A)) & (A @ a))) ).
% 12.95/4.17 thf(5,axiom,((setunion @ c @ a)),file('/export/starexec/sandbox/benchmark/theBenchmark.p',ca)).
% 12.95/4.17 thf(12,plain,((? [A:($i > $o)]: ((c @ (A)) & (A @ a)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 12.95/4.17 thf(13,plain,(((c @ (sk1)) & (sk1 @ a))),inference(cnf,[status(esa)],[12])).
% 12.95/4.17 thf(15,plain,((sk1 @ a)),inference(cnfConj,[status(thm)],[13])).
% 12.95/4.17 thf(92,axiom,((? [A:(($i > $o) > $i)]: ! [B:($i > $o)]: ((? [C:$i]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 12.95/4.17 thf(376,plain,(! [A:$i] : ((~ (sk1 @ A)) | (sk1 @ (eps @ (sk1))))),inference(choice,[status(esa)],[92])).
% 12.95/4.17 thf(389,plain,(! [A:$i] : (~ (($true)) | (sk1 @ (eps @ (sk1))) | ((sk1 @ a) != (sk1 @ A)))),inference(paramod_ordered,[status(thm)],[15,376])).
% 12.95/4.17 thf(390,plain,(! [A:$i] : ((sk1 @ (eps @ (sk1))) | ((sk1 @ a) != (sk1 @ A)))),inference(simp,[status(thm)],[389])).
% 12.95/4.17 thf(391,plain,((sk1 @ (eps @ (sk1)))),inference(pattern_uni,[status(thm)],[390:[bind(A, $thf(a))]])).
% 12.95/4.17 thf(20,axiom,((? [A:((($i > $o) > $o) > ($i > $o))]: ! [B:(($i > $o) > $o)]: ((? [C:($i > $o)]: (B @ C)) => (B @ (A @ B))))),introduced(axiom_of_choice)).
% 12.95/4.17 thf(21,plain,(! [A:($i > $o)] : ((~ ((c @ (A)) & (A @ (eps @ (A))))) | ((c @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))))) & (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ (eps @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))))))))),inference(choice,[status(esa)],[20])).
% 12.95/4.17 thf(23,plain,(! [A:($i > $o)] : (((~ (c @ (A)) | ~ (A @ (eps @ (A))) | (c @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B))))))) & (~ (c @ (A)) | ~ (A @ (eps @ (A))) | (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ (eps @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B))))))))))),inference(cnf,[status(esa)],[21])).
% 12.95/4.17 thf(25,plain,(! [A:($i > $o)] : ((~ (c @ (A))) | (~ (A @ (eps @ (A)))) | (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ (eps @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B))))))))),inference(cnfConj,[status(thm)],[23])).
% 12.95/4.17 thf(419,plain,(! [A:($i > $o)] : ((~ (c @ (A))) | ~ (($true)) | (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ (eps @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B))))))) | ((sk1 @ (eps @ (sk1))) != (A @ (eps @ (A)))))),inference(paramod_ordered,[status(thm)],[391,25])).
% 12.95/4.17 thf(420,plain,(! [A:($i > $o)] : ((~ (c @ (A))) | (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ (eps @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B))))))) | ((sk1 @ (eps @ (sk1))) != (A @ (eps @ (A)))))),inference(simp,[status(thm)],[419])).
% 12.95/4.17 thf(424,plain,((~ (c @ (sk1))) | (epsio @ (^ [A:($i > $o)]: ((c @ A) & (A @ (eps @ A)))) @ (eps @ (epsio @ (^ [A:($i > $o)]: ((c @ A) & (A @ (eps @ A)))))))),inference(pre_uni,[status(thm)],[420:[bind(A, $thf(sk1))]])).
% 12.95/4.17 thf(1,conjecture,(((c @ (choosenonempty @ c)) & ? [A:$i]: (choosenonempty @ c @ A))),file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 12.95/4.17 thf(2,negated_conjecture,((~ ((c @ (choosenonempty @ c)) & ? [A:$i]: (choosenonempty @ c @ A)))),inference(neg_conjecture,[status(cth)],[1])).
% 12.95/4.17 thf(6,plain,((~ ((c @ (epsio @ (^ [A:($i > $o)]: ((c @ A) & (A @ (eps @ A)))))) & ? [A:$i]: (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 12.95/4.17 thf(7,plain,(! [A:$i] : ((~ (c @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B))))))) | (~ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ A)))),inference(cnf,[status(esa)],[6])).
% 12.95/4.17 thf(14,plain,((c @ (sk1))),inference(cnfConj,[status(thm)],[13])).
% 12.95/4.17 thf(24,plain,(! [A:($i > $o)] : ((~ (c @ (A))) | (~ (A @ (eps @ (A)))) | (c @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))))))),inference(cnfConj,[status(thm)],[23])).
% 12.95/4.17 thf(73,plain,(! [A:($i > $o)] : (~ (($true)) | (~ (A @ (eps @ (A)))) | (c @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))))) | ((c @ (sk1)) != (c @ (A))))),inference(paramod_ordered,[status(thm)],[14,24])).
% 12.95/4.17 thf(74,plain,(! [A:($i > $o)] : ((~ (A @ (eps @ (A)))) | (c @ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))))) | ((c @ (sk1)) != (c @ (A))))),inference(simp,[status(thm)],[73])).
% 12.95/4.17 thf(75,plain,((~ (sk1 @ (eps @ (sk1)))) | (c @ (epsio @ (^ [A:($i > $o)]: ((c @ A) & (A @ (eps @ A))))))),inference(pattern_uni,[status(thm)],[74:[bind(A, $thf(sk1))]])).
% 12.95/4.17 thf(409,plain,(~ (($true)) | (c @ (epsio @ (^ [A:($i > $o)]: ((c @ A) & (A @ (eps @ A))))))),inference(rewrite,[status(thm)],[75,391])).
% 12.95/4.17 thf(410,plain,((c @ (epsio @ (^ [A:($i > $o)]: ((c @ A) & (A @ (eps @ A))))))),inference(simp,[status(thm)],[409])).
% 12.95/4.17 thf(431,plain,(! [A:$i] : (~ (($true)) | (~ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ A)))),inference(rewrite,[status(thm)],[7,410])).
% 12.95/4.17 thf(432,plain,(! [A:$i] : ((~ (epsio @ (^ [B:($i > $o)]: ((c @ B) & (B @ (eps @ B)))) @ A)))),inference(simp,[status(thm)],[431])).
% 12.95/4.17 thf(598,plain,(~ (($true)) | ($false)),inference(rewrite,[status(thm)],[424,432,14])).
% 12.95/4.17 thf(599,plain,(($false)),inference(simp,[status(thm)],[598])).
% 12.95/4.17 % SZS output end Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.95/4.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------