%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : PHI004^8 : TPTP v9.3.1. Released v9.0.0.
% 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 : n004.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 08:20:13 AM UTC 2026
% Result : Theorem 3.71s 1.51s
% Output : Refutation 3.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PHI004^8 : TPTP v9.3.1. Released v9.0.0.
% 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
% 0.10/0.23 % Computer : n004.cluster.edu
% 0.10/0.23 % Model : x86_64 x86_64
% 0.10/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.23 % Memory : 8046.5625MB
% 0.10/0.23 % OS : Linux 6.8.0-71-generic
% 0.10/0.23 % CPULimit : 300
% 0.10/0.23 % WCLimit : 300
% 0.10/0.23 % DateTime : Tue Sep 29 13:17:22 UTC 2026
% 0.10/0.24 % CPUTime :
% 0.10/0.24 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
% 0.63/0.54 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.98/0.64 % [INFO] Parsing done (103ms).
% 0.98/0.66 % [INFO] Input problem is non-classical (logic $alethic_modal). Running HOL transformation from semantics specification contained in the problem file ...
% 1.18/0.72 % [INFO] Running in sequential loop mode.
% 1.81/0.92 % [INFO] eprover registered as external prover.
% 1.81/0.92 % [INFO] Scanning for conjecture ...
% 1.81/0.98 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 1.81/1.00 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 1.81/1.01 % [INFO] Problem is higher-order (TPTP THF).
% 1.81/1.02 % [INFO] Type checking passed.
% 1.81/1.02 % [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 ...
% 3.71/1.51 % External prover 'e' found a proof!
% 3.71/1.51 % [INFO] Killing All external provers ...
% 3.71/1.51 % Time passed: 1187ms (effective reasoning time: 781ms)
% 3.71/1.51 % 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)>
% 3.71/1.51 % Axioms used in derivation (5): a4, mrel_universal, a3, a1, a2
% 3.71/1.51 % No. of inferences in proof: 14
% 3.71/1.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1187 ms resp. 781 ms w/o parsing
% 3.71/1.55 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.71/1.55 thf(mworld_type, type, mworld: $tType).
% 3.71/1.55 thf(mrel_decl, type, mrel: (mworld > (mworld > $o))).
% 3.71/1.55 thf(mbox_decl, type, mbox: ((mworld > $o) > (mworld > $o))).
% 3.71/1.55 thf(mactual_decl, type, mactual: mworld).
% 3.71/1.55 thf(mlocal_decl, type, mlocal: ((mworld > $o) > $o)).
% 3.71/1.55 thf(mglobal_decl, type, mglobal: ((mworld > $o) > $o)).
% 3.71/1.55 thf(positive_decl, type, positive: (mworld > (($i > $o) > $o))).
% 3.71/1.55 thf(godlike_decl, type, godlike: (mworld > ($i > $o))).
% 3.71/1.55 thf(essence_decl, type, essence: (mworld > (($i > $o) > ($i > $o)))).
% 3.71/1.55 thf(mbox_def, definition, mbox = (^ [A:(mworld > $o),B:mworld]: ! [C:mworld]: ((mrel @ B @ C) => (A @ C))) ).
% 3.71/1.55 thf(mlocal_def, definition, mlocal = (^ [A:(mworld > $o)]: (A @ mactual)) ).
% 3.71/1.55 thf(mglobal_def, definition, mglobal = ((!) @ mworld) ).
% 3.71/1.55 thf(godlike_def, definition, godlike = (^ [A:mworld,B:$i]: ! [C:($i > $o)]: ((positive @ A @ C) => (C @ B))) ).
% 3.71/1.55 thf(essence_def, definition, essence = (^ [A:mworld,B:($i > $o),C:$i]: ((B @ C) & ! [D:($i > $o)]: ((D @ C) => (mbox @ (^ [E:mworld]: ! [F:$i]: ((B @ F) => (D @ F))) @ A)))) ).
% 3.71/1.55 thf(5,axiom,((mglobal @ (^ [A:mworld]: ! [B:($i > $o),C:($i > $o)]: (((positive @ A @ B) & (mbox @ (^ [D:mworld]: ! [E:$i]: ((B @ E) => (C @ E))) @ A)) => (positive @ A @ C))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 3.71/1.55 thf(24,plain,((! [A:mworld,B:($i > $o),C:($i > $o)]: (((positive @ A @ (B)) & ! [D:mworld]: ((mrel @ A @ D) => (! [E:$i]: ((B @ E) => (C @ E))))) => (positive @ A @ (C))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[5])).
% 3.71/1.55 thf(4,axiom,((mglobal @ (^ [A:mworld]: ! [B:($i > $o)]: ((positive @ A @ (^ [C:$i]: ~ (B @ C))) = (~ (positive @ A @ B)))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1)).
% 3.71/1.55 thf(21,plain,((! [A:mworld,B:($i > $o)]: ((positive @ A @ (^ [C:$i]: ~ (B @ C))) = (~ (positive @ A @ (B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[4])).
% 3.71/1.55 thf(7,axiom,((mglobal @ (^ [A:mworld]: ! [B:($i > $o)]: ((positive @ A @ B) => (mbox @ (^ [C:mworld]: (positive @ C @ B)) @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4)).
% 3.71/1.55 thf(32,plain,((! [A:mworld,B:($i > $o)]: ((positive @ A @ (B)) => (! [C:mworld]: ((mrel @ A @ C) => (positive @ C @ (B))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[7])).
% 3.71/1.55 thf(1,conjecture,((mlocal @ (^ [A:mworld]: ! [B:$i]: ((godlike @ A @ B) => (essence @ A @ (godlike @ A) @ B))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2)).
% 3.71/1.55 thf(2,negated_conjecture,((~ (mlocal @ (^ [A:mworld]: ! [B:$i]: ((godlike @ A @ B) => (essence @ A @ (godlike @ A) @ B)))))),inference(neg_conjecture,[status(cth)],[1])).
% 3.71/1.55 thf(8,plain,((~ (! [A:$i]: ((! [B:($i > $o)]: ((positive @ mactual @ (B)) => (B @ A))) => (! [B:($i > $o)]: ((positive @ mactual @ (B)) => (B @ A)) & ! [B:($i > $o)]: ((B @ A) => (! [C:mworld]: ((mrel @ mactual @ C) => (! [D:$i]: ((! [E:($i > $o)]: ((positive @ mactual @ (E)) => (E @ D))) => (B @ D))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
% 3.71/1.55 thf(6,axiom,((mglobal @ (^ [A:mworld]: (positive @ A @ (godlike @ A))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 3.71/1.55 thf(30,plain,((! [A:mworld]: (positive @ A @ (^ [B:$i]: ! [C:($i > $o)]: ((positive @ A @ C) => (C @ B)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[6])).
% 3.71/1.55 thf(3,axiom,((! [A:mworld,B:mworld]: (mrel @ A @ B))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_universal)).
% 3.71/1.55 thf(19,plain,((! [A:mworld,B:mworld]: (mrel @ A @ B))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[3])).
% 3.71/1.55 thf(48,plain,(($false)),inference(e,[status(thm)],[24,21,32,8,30,19])).
% 3.71/1.55 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.71/1.55 % [INFO] Killing All external provers ...
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