%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI046^10 : TPTP v9.3.1. Released v9.1.0.
% 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 : 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 08:20:15 AM UTC 2026
% Result : Theorem 4.18s 1.82s
% Output : Refutation 4.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PHI046^10 : TPTP v9.3.1. Released v9.1.0.
% 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
% 0.10/0.20 % Computer : n017.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 13:15:52 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
% 0.66/0.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.90/0.62 % [INFO] Parsing done (103ms).
% 1.07/0.64 % [INFO] Input problem is non-classical (logic $modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.28/0.70 % [INFO] Running in sequential loop mode.
% 1.91/0.90 % [INFO] eprover registered as external prover.
% 1.91/0.90 % [INFO] Scanning for conjecture ...
% 1.91/0.99 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.19/1.03 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.19/1.09 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.10 % [INFO] Type checking passed.
% 2.19/1.10 % [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 ...
% 4.18/1.82 % External prover 'e' found a proof!
% 4.18/1.82 % [INFO] Killing All external provers ...
% 4.18/1.82 % Time passed: 1522ms (effective reasoning time: 1111ms)
% 4.18/1.82 % 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)>
% 4.18/1.82 % Axioms used in derivation (5): axiomV1star, axiomV2, mrel_symmetric, axiomV3star, axiomV4
% 4.18/1.82 % No. of inferences in proof: 14
% 4.18/1.82 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1522 ms resp. 1111 ms w/o parsing
% 4.18/1.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.88 thf(individual_type, type, individual: $tType).
% 4.18/1.88 thf(mworld_type, type, mworld: $tType).
% 4.18/1.88 thf(mrel_decl, type, mrel: (mworld > (mworld > $o))).
% 4.18/1.88 thf(mbox_decl, type, mbox: ((mworld > $o) > (mworld > $o))).
% 4.18/1.88 thf(mactual_decl, type, mactual: mworld).
% 4.18/1.88 thf(mlocal_decl, type, mlocal: ((mworld > $o) > $o)).
% 4.18/1.88 thf(mglobal_decl, type, mglobal: ((mworld > $o) > $o)).
% 4.18/1.88 thf(positive_decl, type, positive: (mworld > ((individual > $o) > $o))).
% 4.18/1.88 thf(godlike_decl, type, godlike: (mworld > (individual > $o))).
% 4.18/1.88 thf(exists_decl, type, exists: (mworld > (individual > $o))).
% 4.18/1.88 thf(mbox_def, definition, mbox = (^ [A:(mworld > $o),B:mworld]: ! [C:mworld]: ((mrel @ B @ C) => (A @ C))) ).
% 4.18/1.88 thf(mlocal_def, definition, mlocal = (^ [A:(mworld > $o)]: (A @ mactual)) ).
% 4.18/1.88 thf(mglobal_def, definition, mglobal = ((!) @ mworld) ).
% 4.18/1.88 thf(exists_def, definition, exists = (^ [A:mworld,B:individual]: ? [C:individual]: ((exists @ A @ C) & (B = C))) ).
% 4.18/1.88 thf(3,axiom,((! [A:mworld,B:mworld]: ((mrel @ A @ B) => (mrel @ B @ A)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_symmetric)).
% 4.18/1.88 thf(10,plain,((! [A:mworld,B:mworld]: ((mrel @ A @ B) => (mrel @ B @ A)))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 4.18/1.88 thf(5,axiom,((mglobal @ (^ [A:mworld]: ! [B:(individual > $o)]: ~ (positive @ A @ (^ [C:individual]: ((B @ C) & ~ (B @ C))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiomV2)).
% 4.18/1.88 thf(20,plain,((! [A:mworld]: ~ (positive @ A @ (^ [B:individual]: (($false)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 4.18/1.88 thf(4,axiom,((mglobal @ (^ [A:mworld]: ! [B:(individual > $o)]: ((mbox @ (^ [C:mworld]: ! [D:individual]: ((exists @ C @ D) => ((B @ D) = ((B @ D) & ~ (B @ D))))) @ A) => ((positive @ A @ B) = (positive @ A @ (^ [C:individual]: ((B @ C) & ~ (B @ C))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiomV1star)).
% 4.18/1.88 thf(12,plain,((! [A:mworld,B:(individual > $o)]: ((! [C:mworld]: ((mrel @ A @ C) => (! [D:individual]: ((exists @ C @ D) => (~ (B @ D)))))) => ((positive @ A @ (B)) = (positive @ A @ (^ [C:individual]: (($false)))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 4.18/1.88 thf(1,conjecture,((mlocal @ (^ [A:mworld]: ? [B:individual]: ((exists @ A @ B) & (godlike @ A @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theoremV6)).
% 4.18/1.88 thf(2,negated_conjecture,((~ (mlocal @ (^ [A:mworld]: ? [B:individual]: ((exists @ A @ B) & (godlike @ A @ B)))))),inference(neg_conjecture,[status(cth)],[1])).
% 4.18/1.88 thf(8,plain,((~ (? [A:individual]: ((exists @ mactual @ A) & (godlike @ mactual @ A))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 4.18/1.88 thf(7,axiom,((mglobal @ (^ [A:mworld]: (positive @ A @ (^ [B:individual]: ((godlike @ A @ B) & (exists @ A @ B))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiomV4)).
% 4.18/1.88 thf(26,plain,((! [A:mworld]: (positive @ A @ (^ [B:individual]: ((godlike @ A @ B) & (exists @ A @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 4.18/1.88 thf(6,axiom,((mglobal @ (^ [A:mworld]: ! [B:individual]: ((exists @ A @ B) => ((godlike @ A @ B) => (! [C:(individual > $o)]: ((positive @ A @ C) => (mbox @ (^ [D:mworld]: (C @ B)) @ A)))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiomV3star)).
% 4.18/1.88 thf(23,plain,((! [A:mworld,B:individual]: ((exists @ A @ B) => ((godlike @ A @ B) => (! [C:(individual > $o)]: ((positive @ A @ (C)) => (! [D:mworld]: ((mrel @ A @ D) => (C @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 4.18/1.88 thf(32,plain,(($false)),inference(e,[status(thm)],[10,20,12,8,26,23])).
% 4.18/1.88 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.18/1.88 % [INFO] Killing All external provers ...
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